Volkhard F. Müller
For a linear Dirac field on a globally hyperbolic static space-time the analytic continuation of its Wightman functions (Green functions) to Schwinger functions and back at zero and finite temperature is shown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
It is an article of folklore that the collection of ideas identified as Euclidean quantum gravity may be derived from ordinary Lorentzian signature gravity by the procedure of Wick rotation. This note will attempt to shed some light on this relatively ill-understood procedure. I argue that it proves inappropriate and unhelpful to regard Wick rotation in terms of a complex deformation of the time coordinate. Rather, Wick rotation can more usefully be viewed as a complex deformation of the spacetime metric. This simple reformulation of the Wick rotation procedure, while it leaves flat space phys…
Recently we proposed a new Wick rotation for Dirac spinors which resulted in a hermitean action in Euclidean space. Our work was in a path integral context, however, in this note, we provide the canonical formulation of the new Wick rotation along the lines of the proposal of Osterwalder and Schrader.
We obtain a continuous Wick rotation for Dirac, Majorana and Weyl spinors $ψ\to \exp ({1\over 2} θγ^4 γ^5)ψ$ which interpolates between Minkowski and Euclidean field theories.
In order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime, it is necessary to construct Wick polynomials and their time ordered products for the noninteracting theory. A construction of these quantities has recently been given by Brunetti, Fredenhagen, and Kohler, and by Brunetti and Fredenhagen, but they did not impose any ``locality'' or ``covariance'' condition in their constructions. As a consequence, their construction of time ordered products contained ambiguities involving arbitrary functions…
We propose a continuous Wick rotation for Dirac, Majorana and Weyl spinors from Minkowski spacetime to Euclidean space which treats fermions on the same footing as bosons. The result is a recipe to construct a supersymmetric Euclidean theory from any supersymmetric Minkowski theory. This Wick rotation is identified as a complex Lorentz boost in a five-dimensional space and acts uniformly on bosons and fermions. For Majorana and Weyl spinors our approach is reminiscent of the traditional Osterwalder Schrader approach in which spinors are ``doubled'' but the action is not hermitean. However, for…
We investigate some peculiar aspects of the so called Lee-Wick Electrodynamics focusing on physical effects produced by the presence of sources for the vector field. The interactions between stationary charges distributions along parallel branes with arbitrary dimensions is investigated and the energy of a point charge is discussed. Some physical phenomena produced in the vicinity of a Dirac string are also investigated. We consider the Lee-Wick theory for the scalar field, where it can emerge some interesting effects with no counterpart for the vector gauge field theory.
In this paper we discuss some aspects concerning the electromagnetic sector of the abelian Lee-Wick (LW) quantum electrodynamics (QED). Using the Dirac's theory of constrained systems, the higher-order canonical quantization of the LW electromagnetism is performed. A quantum bound on the LW heavy mass is also estimated using the best known measurement of the anomalous magnetic moment of the electron. Finally it is shown that magnetic monopoles can coexist peacefully in the LW scenario.
Very recently, the Lee-Wick standard model has been introduced as a non-SUSY extension of the Standard model which solves the Hierarchy problem. In this model, each field kinetic term attains a higher derivative term. Like any Lee-Wick theory, this model suffers from existence of Ghost states. In this work, we consider a prototype scalar field theory with its kinetic term has a higher derivative term, which mimics the scalar sector in the Lee-Wick Standard model. We introduced an imaginary auxiliary field to have an equivalent non-Hermitian two-field scalar field theory. We were able to calcul…
We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and the correlators extend analytically to a certain domain of complex-valued metrics. Ordinary Riemannian metrics are contained in the allowable domain, while Lorentzian metrics lie on its boundary.
We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without electric fields, and imply that the spheres will collapse toward zero size. We then go on to consider the $D1-D3$ intersection in a curved background and find various dualities and automorphisms of the general equations of motion. It is possible to map the dynamical equation of motion to the static one via Wick rotation, however the additional spatial dependen…
Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant symplectic structure, which can serve as a starting point for a phase space quantization of such objects. Some open questions for further research are outlined.
In this article we review the quantization of the Dirac-field on a curved spacetime. For that purpose we describe the construction of the local observable algebras in the algebraic approach to quantum field theory. Among the possible states we single out the so called Hadamard-states, which are the ones relevant for physics. Finally, as an example, we give a definition for an adiabatic vacuum state of the Dirac-field on a Robertson-Walker spacetime. We believe that these states are physical in the sense that they have the singularity structure of Hadamard-form, although we cannot give a formal…
Hollands and Wald's technique based on *-algebras of Wick products of field operators is strightforwardly generalized to define the stress-energy tensor operator in curved globally hyperbolic spacetimes. In particular, the locality and covariance requirement is generalized to Wick products of differentiated quantum fields. The proposed stress-energy tensor operator is conserved and reduces to the classical form if field operators are replaced by classical fields satisfying the equation of motion. The definition is based on the existence of convenient counterterms given by certain local Wick pr…
The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered products. It is shown that the Wick powers may be defined such that the current and the stress-energy tensor are conserved, and the remaining ambiguity is characterized. We sketch a variant of the background field method that can be used to determine the renormalization group flow at the one loop level from the nontrivial scaling of Wick powers.
I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the coefficients themselves in powers of the coupling constants, this formula allows to compute them recursively to arbitrary order. As input, only the OPE coefficients in the free theory are needed, which are easily obtained using Wick's theorem. I illustrate the method by computing the OPE of two scalars $ϕ$ in hyperbolic space (Euclidean Anti-de Sitter space) u…
In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time-dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possib…
Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM) and the Dirac-bracket formulation in the case of the derivative-type constraint. Using the successive projection procedure and the iterativity of the Dirac bracket, the noncommutative quantum system is constructed in the form including all orders of the noncommutativity-parameters. When the noncommutative quantum system is constrained to a curved space, the …
Unitarity Violation in Field Theories of Lee-Wick's Complex Ghost
本文在算符形式体系中研究Lee-Wick四阶导数理论的幺正性问题，证明复鬼粒子实际会被产生并破坏幺正性，同时发现存在一个能量阈值，低于该阈值时理论保持幺正且可重整化。
Compatibility of symmetric quantization of the Dirac equation in a curved space with general covariance gives a special representation of the spin connections in which their dot product with the Dirac gamma matrices becomes equal to the "covariant divergence" of the latter. Requiring that the square of the equation gives the conventional Klein-Gordon equation in a curved space results in an operator algebra for the Dirac gamma matrices that involves the "covariant derivative" connections and the Riemann-Christoffel connections. In 1+1 space-time with static metric, we obtain exact solutions of…
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries, both for the full Dirac equation and for its semi-classical limit, the spinning particle. A concrete application of the general results is provided by the case of rotating higher dimensional black holes with cosmological constant, which we discuss. For these metrics the Dirac equation is separable and the relation between this and hidden symmetries is explain…
Remarks on four dimensional Euclidean gravity without Wick rotation
本文针对 Hawking 提出的无 Wick 旋转四维欧几里得量子引力方案，引入圆锥 sedenion 数系作为计算工具，以同时容纳双曲与欧几里得度规并辅助描述量子引力。
Diverse theories of Quantum Gravity expect modification of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle.It was shown by some authors that the Generalized uncertainty principle gives rise to corrections to Schrodinger,Klien-Gordon and Dirac equations.By solving the Generalized uncertainty principle corrected equations,the authors arrived at quantization not only of energy but also of box length,area and volume. We extend the above result to the case of curved Space-Time(Schwarzschild metric). We showed that we arrived at the Quantiz…
The Dirac oscillator in the curved spacetime of a cloud of strings
研究弦云曲空间中狄拉克振子的束缚态解，通过四分量规范狄拉克旋量和相对论能谱得到能量谱，分析其依赖于角频率、曲率参数和有效静质量的量子化特性。
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to λ^2 \g$. We consider explicitly the case of a scalar field, $ϕ$, with a self-interaction of the form $κϕ^4$, although our results should generalize straightforwardly to other renormalizable theories. We construct the interacting field--as well as its Wick powers and their time-ordered-products--as formal power series in the algebra generated by the Wick powers and time-ordered-products of the free field, and we determine the…
Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized sine-Gordon model, both living in $1+1$-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.
Non-relativistic limit of scalar and Dirac fields in curved spacetime
本文从第一性原理推导弯曲时空中标量场与Dirac场的非相对论极限，得到Schrödinger-Newton理论的广义相对论修正，并在Rindler时空中表明高加速度下引力—自旋耦合使Dirac粒子更适合观测非牛顿引力。
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime described by conformally flat metric. Also, supersymmetric quantum mechanics is used both to factorize the Dirac Hamiltonians and obtain new metric functions. Finally, it is observed that the energy dependent potentials may be extended to the energy dependent metric functions.
A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample.
Feshbach-Villars Formalism for a Spin-1/2 Particle in Curved Spacetime
本研究提出在弯曲时空中自旋1/2粒子的费舍巴-维拉尔斯形式化，推导了狄拉克方程的哈密顿形式，并探讨了引力和电磁相互作用下的量子力学框架。
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a common geometrical framework and we prove theorems that relate together the different representations and the different choices of connections. In particular, the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the Dirac equation for a vector wave function, in the same spacetime.
We discuss a new realization of $\mathcal{N}$-extended quantum-mechanical supersymmetry (QM SUSY) with central charges hidden in the four-dimensional (4D) mass spectrum of higher dimensional Dirac action with curved extra dimensions. We show that this $\mathcal{N}$-extended QM SUSY results from symmetries in extra dimensions, and the supermultiplets in this supersymmetry algebra correspond to the Bogomol'nyi--Prasad--Sommerfield states. Furthermore, we examine the model of the $S^2$ extra dimension with a magnetic monopole background and confirm that the $\mathcal{N}$-extended QM SUSY explains…
Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to lattice strain. We show this is incorrect by using a real space gradient expansion to study how the Dirac equation derives from the tight binding model. Generic spatially varying hopping functions give rise to large magnetic fields which spoil the truncation in derivatives. In the perturbative regime, the only consistent truncation to Dirac is one with nontrivial …
We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem, so our construction essentially completes the analysis of the existence, uniqueness and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime. As a byproduct of our analysis, we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in…
Dirac equation in curved spacetime: the role of local Fermi velocity
本文研究了带电载流子在存在局部费米速度的弯曲狄拉克材料中的运动，给出了纳米卷曲柱面几何中该物理量的显式参数化，并讨论了相关的物理效应与可观测性质。
We review the geodesic motion of pseudo-classical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. The gravitational and axial anomalies are studied for generalized Euclidean Taub-NUT me…
We use the Wick-rotated time-dependent supersymmetry to construct models of two-dimensional Dirac fermions in presence of an electrostatic grating. We show that there appears omnidirectional perfect transmission through the grating at specific energy. Additionally to being transparent for incoming fermions, the grating hosts strongly localized states.
In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated in both Cartesian and curvilinear coordinates. The energy spectrum of the multidimensional rotator is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere.
We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy. These criteria turn out to be restrictive, but they do not fix a unique construction: two of our operators generally satisfy the axioms, and we provide an explicit example where they are inequivalent. For highly symmetric spacetimes with Drinfeld twists constructed from sufficiently many Killing vector fields, all of our operators coincide. For ge…
A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type equation. Their components are scalar, pseudo-scalar, vector, axial-vector fields and fields strength which satisfy an irreducible systems of first-order Dirac-Kahler equations having remarkable gauge and duality properties similar to those of the flat case. The vector and axial-vector fields are the physical potentials giving rise to the field strength while th…
We argue that the Fermi-Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields, is exactly equivalent to the gauge theory Hamiltonian describing Dirac fermions in the lattice. We show that it is possible to couple the Dirac fermions to an "artificial" gravitational field, i.e. to consider the Dirac physics in a curved spacetime. We identify the special class of spacetime metrics that admit a simple realization in terms of a Fermi-Hubbard model subjected to an artificial SU(2) field, corresponding to position depe…
Nonlocal Dirac theory in curved spacetime and the Bunch--Davies vacuum
本文构建弯曲时空中的非局域自旋-1/2场论，推导非局域狄拉克方程，并在德西特时空构造非局域Bunch--Davies模式，证明其解析结构保持且可平滑回归局域理论。
We study the coupling of a 2+1 dimensional non-relativistic spin 1/2 fermion to a curved Newton-Cartan geometry, using null reduction from an extra-dimensional relativistic Dirac action in curved spacetime. We analyze Weyl invariance in detail: we show that at the classical level it is preserved in an arbitrary curved background, whereas at the quantum level it is broken by anomalies. We compute the trace anomaly using the Heat Kernel method and we show that the anomaly coefficients a, c are proportional to the relativistic ones for a Dirac fermion in 3+1 dimensions. As for the previously stud…
Neutrino Oscillations without Mass: A Re-analysis of KamLAND Data following the Dirac Equation in Curved Spacetime
基于弯曲时空狄拉克方程，将无质量中微子味态建模为能量依赖的两能级量子态，重新分析KamLAND数据，获得比标准有质量中微子范式更高的似然拟合。
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact in mind, the following problem is studied in this work: when a spin 1/2 particle is constrained to move on a curved surface, is it possible to describe this particle without giving reference to the dimensions external to the surface? As a special case of this, a relativistic spin 1/2 particle which is constrained to move on a 2 + 1 dimensional hypersurface …
The Dirac Hamiltonian in the (2+1) dimensional curved space-time has been studied with a metric for an expanding de Sitter space-time which is a two sphere. The spectrum and the exact solutions of the time dependent non-Hermitian and angle dependent Hamiltonians are obtained in terms of the Jacobi and Romanovski polynomials. Hermitian equivalent of the Hamiltonian obtained from the Dirac equation is discussed in the frame of pseudo-Hermiticity. Furthermore, pseudo-supersymmetric quantum mechanical techniques are expanded to a curved Dirac Hamiltonian and a partner curved Dirac Hamiltonian is g…
Circuit realization of tilted Dirac cone: A platform for fabrication of curved spacetime geometry on a chip
提出一种支持倾斜狄拉克锥的LC电路模型，通过阻抗谱测量互感与电容参数以获取背景时空度规信息，为在芯片上制备弯曲时空几何提供了平台。
We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with the current conservation: we show that the latter applies to any solution of the Dirac equation, iff the field of Dirac matrices $γ^μ$ satisfies a specific PDE. This equation is always satisfied for DFW …
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat bot…
A chiral alternative to the vierbein field in general relativity was considered by 't Hooft in an attempt to facilitate the construction of a quantum theory of gravity. These objects $ f^a{}_{μν}$ behave like the "cube root" of the metric tensor. We try to construct specific representations of these tensors in terms of Dirac $γ$ matrices in Euclidean and Minkowski space, and promote these to curved space through Newman-Penrose formalism. We conjecture that these are new objects with physical significance and are the analog of Killing-Yano tensors. As an application, we try to construct non-Abe…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting results, leading to the question of whether the canonical approach is covariant, and whether the path integral approach is unitary. We show the unitarity of the covariant U(1) Maxwell theory, defined via the Wick rotation of a Euclidean path integral. We begin by gauge-fixing the path integral, taking care with zero modes, large gauge transformations, and nontriv…
This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fields are pictured as sections of natural vector bundles over globally hyperbolic spacetimes and quantized through the known functorial machinery in terms of local $^*$-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles, in addition to the Lorentzian metric. The mass and the coupling constants are in particular viewed as backgrou…
We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple ``Principle of Perturbative Agreement'': For interaction Lagrangians $L_1$ that are such that the interacting field theory can be constructed exactly--as occurs when $L_1$ is a ``pure divergence'' or when $L_1$ is at most quadratic in the field and contains no more than two derivatives--then time-ordered products must be defined so that the perturbative solutio…
It has been shown that, for all dimensions and signatures, the most general first-order linear symmetry operators for the Dirac equation including interaction with Maxwell field in curved background are given in terms of Killing-Yano (KY) forms. As a general gauge invariant condition it is found that among all KY-forms of the underlying (pseudo) Riemannian manifold, only those which Clifford commute with the Maxwell field take part in the symmetry operator. It is also proved that associated with each KY-form taking part in the symmetry operator, one can define a quadratic function of velocitie…
The Yukawa model in curved spacetime is considered. We consider a complex scalar field coupled to a $U(1)$ gauge field and also interacting with Dirac fields with a general Yukawa coupling. The local momentum space method is used to obtain the one-loop effective action and we adopt the gauge condition independent background field method introduced by Vilkovisky and DeWitt. The pole parts of the one-loop effective action that depend on the background scalar field, that we do not assume to be constant, are found and used to calculate the counterterms and to determine the relevant renormalization…
We show that a free Dirac quantum field on a globally hyperbolic spacetime has the following structural properties: (a) any two quasifree Hadamard states on the algebra of free Dirac fields are locally quasiequivalent; (b) the split-property holds in the representation of any quasifree Hadamard state; (c) if the underlying spacetime is static, then the nuclearity condition is satisfied, that is, the free energy associated with a finitely extended subsystem (``box'') has a linear dependence on the volume of the box and goes like $\propto T^{s+1}$ for large temperatures $T$, where $s+1$ is the n…
In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the corresponding Dirac-Weyl spinors in a given empty spacetime. Regarding them as basic units, other higher spin massless free-field spinors are then identified. Along this way, we find some hidden fundamental features related to these fields. In particular, for non-twisting vacuum Petrov type N solutions, we show that all higher spin massless free-field spinor…
We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields leads to an equivalent Hamiltonian operator H, or to an equivalent energy operator E. We do that for the standard version of the gravitational Dirac equation, and for two alternative equations based on the tensor representation of the Dirac fields. The latter equations may be defined when the spacetime is four-dimensional, noncompact, and admits a spinor struc…
In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank two, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is…
Completing the results obtained in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth $D$-dimensional Lorentzian manifolds. To this end, it is shown that, in any Lorentzian manifold, a sort of ``local Wick rotation'' of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinates are ``physical''. No time-like Killing field is necessary. Such a local Wick rotation analytically continues the Lorentzian metric in a neighborhood of any point, or, more generally, in a neighborhood of a space…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。