Link between quantum measurement and the iε term in the QFT propagator

Relativistic bound-state equations for two-fermion systems

We point out that the free single-fermion propagator which is used in the QFT equations for two-fermion systems, has a bosonic structure, transforms to the single-boson propagator for the Klein-Gordon equation in the nonrelativistic limit, and, therefore, does not satisfy the Lehmann spectral representation for fermions. Proceeding from the Lippmann-Schwinger integral equation, we obtain a two-fermion relativistic wave equation in which the free two-fermion equal-time propagator satisfying the Lehmann representation, is used. This wave equation has been applied to the electron-positron system.…

Propagators of Generalized Schrödinger Equations Related by Higher-Order Supersymmetry

We construct explicit integral relations between propagators of generalized Schrödinger equations that are linked by higher-order supersymmetry. Our results complement and extend the findings obtained in J. Phys.A 40, 10557 (2007) for the conventional Schrödinger equation.

关系量子场论基础 I：标量场

Foundations of Relational Quantum Field Theory I: Scalars

本文基于操作量子参考框架，在相对论背景下构建了关系量子场论的基础，探讨了标量场中关系局部可观测量和点场的出现，以及与Wightman场论的对比。

Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

We present a holographic construction of solutions to the gravitational wave equation starting from QFT scattering amplitudes. The construction amounts to a change of basis from momentum to $(2,2)$ twistor space, together with a recently introduced analytic continuation between $(2,2)$ and $(1,3)$ spacetimes. We test the transform for three and four-point amplitudes in a classical limit, recovering both stationary and dynamical solutions in GR as parametrized by their tower of multipole moments, including the Kerr black hole. As a corollary, this provides a link between the Kerr-Schild classic…

Lecture Notes on Three Supersymmetric/Topological Systems in Quantum Field Theory

((1+1)-dimensional ${\cal N}=1$ super-symmetric field theory and (3+1)-dimensional ${\cal N}=2$ super-symmetric gauge theory are discussed in a, more or less, unified way, designed to identify the quantum BPS states in both systems. Euclidean 4-dimensional gauge theory with ${\cal N}=2$ twisted super-symmetry is also analized. ${\bf C}^\infty$-topological invariants are identified as certain n-point correlation functions in this QFT framework. The twist of the effective dual Abelian gauge theory is briefly described, both from mathematical and physical viewpoints. The physical nature of the to…

Pascual Jordan's legacy and the ongoing research in quantum field theory

Pascual Jordan's path-breaking role as the protagonist of quantum field theory (QFT) is recalled and his friendly dispute with Dirac's particle-based relativistic quantum theory is presented as the start of the field-particle conundrum which, though in modified form, persists up to this date. Jordan had an intuitive understanding that the existence of a causal propagation with finite propagation speed in a quantum theory led to radically different physical phenomena than those of QM. The conceptional-mathematical understanding for such an approach began to emerge only 30 years later. The stron…

Boundary-to-bulk maps for AdS causal wedges and RG flow

We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS$_{d+1}$ down to the unitary bound $Δ=(d-2)/2$. That is to say, we construct the `smearing functions' $K$ of HKLL but with different boundary conditions where both dimensions $Δ_+$ and $Δ_-$ are taken into account. More precisely, we impose Robin boundary conditions, which interpolate between Dirichlet and Neumann boundary conditions and we give explicit expressions for the distributional kernel $K$ with spacelike support. This flow between boundary conditions is known to be captured in the boundary by a…

Paths of Canonical Transformations and their Quantization

In their simplest formulations, classical dynamics is the study of Hamiltonian flows and quantum mechanics that of propagators. Both are linked, and emerge from the datum of a single classical concept, the Hamiltonian function. We study and emphasize the analogies between Hamiltonian flows and quantum propagators; this allows us to verify G. Mackey's observation that quantum mechanics (in its Weyl formulation) is a refinement of Hamiltonian mechanics. We discuss in detail the metaplectic representation, which very explicitly shows the close relationship between classical mechanics and quantum …

$\mathcal{S}$-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral…