S-Wave Scattering of Fermion Revisited

Soft Radiation from Scattering Amplitudes Revisited

We apply the recently developed formalism by Kosower, Maybee and O'Connell (KMO) to analyse the soft electromagnetic and soft gravitational radiation emitted by particles without spin in Four and higher dimensions. We use this formalism in conjunction with quantum soft theorems to derive radiative electro-magnetic and gravitational fields in low frequency expansion and to next to leading order in the coupling. We show that in all dimensions, the classical limit of sub-leading soft (photon and graviton) theorems is consistent with the classical soft theorems proved by Sen et al in a series of p…

Fermion number of twisted kinks in the NJL$_2$ model, revisited

As a consequence of axial current conservation, fermions cannot be localized in the massless NJL$_2$ model. In the case of twisted kinks, this manifests itself in a cancellation between valence fermion density and fermion density induced in the Dirac sea. To attribute the correct fermion number to these bound states requires an infrared regularization. Recently, this has been achieved by introducing a bare fermion mass, at least in the non-relativistic regime of small twist angles and fermion numbers. Here, we propose a simpler regularization by a finite box which preserves integrability and c…

Boson-fermion correspondence for Hall-Littlewood polynomials revisited

We connect twisted vertex operator presentation of Hall-Littlewood polynomials with the action of charged free fermions, describe a boson-fermion correspondence that relates twisted vertex operators with classical Heisenberg algebra. We also show that the elements of the orthogonal to Schur functions basis of the one-parameter deformation of the ring of symmetric functions $Λ[t]$ are $τ$-functions of KP hierarchy.

Separation of scattering and selfaction revisited

The definition of scattering operator in Quantum Field Theory is critically reconsidered. The correct treatment of one-particle states is connected with separation of selfaction from interaction. The formalism of functional integral is used for the description of such a separation via introduction of the quantum equation of motion.

再探双荷子的电磁移动

Electromagnetic Scoot for Dyons Revisited

研究双荷子散射，通过在多粒子态表示中比较，将电荷散射电磁移动效应分析扩展到电和磁荷散射，对比纯电荷情况。

Nambu--Jona-Lasinio Model Revisited with a Simple Regularization-Renormalization Method

According to the pioneering model proposed by Nambu and Jona-Lasinio (NJL) \cite{2,3}, a massless fermion acquires its mass via a vacuum phase transition (VPT) process. Our discussion is considerably simplified because an effective Hamiltonian for VPT is proposed and a simple regularization-renormalization method (RRM) is adopted. An unambiguous constraint is found as $\frac{π^2}{GΔ^2_1}=\frac{2}{3}$, where $G$ is the coupling constant first introduced in the NJL model while $Δ_1$ the mass of fermion ($f$) created after the VPT. The masses of bosons with spin-parity $J^P=0^+, 0^-,1^+$ and $1^-…

Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited

We use the recently developed tools for an exact bosonization of a finite number $N$ of non-relativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized hamiltonian naturally splits into an O$(N)$ piece and an O$(1)$ piece. We show that in the large-N and low-energy limit, the O$(N)$ piece in the hamiltonian describes a massless relativistic boson, while the O$(1)$ piece gives rise to cubic self-interactions of the boson. At finite $N$ and high energies, the low-energy effective description breaks down and the exact bosonized hamiltonian …

Anomalous gauge theories revisited

A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, {\it all} anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact $\U(1)$ link variables, while a non-compact formulation is possible at least for the vacuum sector in the…

Lorentz and CPT violation in QED revisited: A missing analysis

We investigate the breakdown of Lorentz symmetry in QED by a CPT violating interaction term consisting of the coupling of an axial fermion current with a constant vector field $b$, in the framework of algebraic renormalization -- a regularization-independent method. We show, to all orders in perturbation theory, that a CPT-odd and Lorentz violating Chern-Simons-like term, definitively, is not radiatively induced by the axial coupling of the fermions with the constant vector $b$.

Three-graviton scattering in Matrix theory revisited

We consider a subset of the terms in the effective potential describing three-graviton interactions in Matrix theory and in classical eleven-dimensional supergravity. In agreement with the results of Dine and Rajaraman, we find that these terms vanish in Matrix theory. We show that the absence of these terms is compatible with the classical supergravity theory when the theory is compactified in a lightlike direction, resolving an apparent discrepancy between the two theories. A brief discussion is given of how this calculation might be generalized to compare the Matrix theory and supergravity …

The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics

We review a recent development in the theoretical understanding of the nu=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore-Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with abelian statistics theta=pi/2, which obey complete spin-charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitude…

$T\bar T$-deformed Fermionic Theories Revisited

We revisit $T\bar T$ deformations of $d=2$ theories with fermions with a view toward the quantization. As a simple illustration, we compute the deformed Dirac bracket for a Majorana doublet and confirm the known eigenvalue flows perturbatively. We mostly consider those $T\bar T$ theories that can be reconstructed from string-like theories upon integrating out the worldsheet metric. After a quick overview of how this works when we add NSR-like or GS-like fermions, we obtain a known non-supersymmetric $T\bar T$ deformation of a $\cN=(1,1)$ theory from the latter, based on the Noether energy-mome…

The open superstring 5-point amplitude revisited

We derive the complete five-gluon scattering amplitude at tree level, within the context of Open Superstring theory. We find the general expression in terms of kinematic factors, and also find its complete expansion up to ${\cal O}({α'}^3)$ terms. We use our scattering amplitude to test three non-equivalent ${\cal O}({α'}^3)$ effective lagrangians that have recently been matter of some controversy.

The massive spinning particle revisited

We propose a formulation of the massive spinning particle in terms of physical bosonic and fermionic fields only. We make use neither of auxiliary objects of the type of $γ_5$ nor of gauge fields. The model is to be used as a suitable starting point for a forthcoming study of the rigid superparticle.

Discrete gauge anomalies revisited

We revisit discrete gauge anomalies in chiral fermion theories in $3+1$ dimensions. We focus on the case that the full symmetry group of fermions is $\mathrm{Spin}(4)\times\mathbb{Z}_n$ or $(\mathrm{Spin}(4)\times\mathbb{Z}_{2m})/\mathbb{Z}_{2}$ with $\mathbb{Z}_2$ being the diagonal $\mathbb{Z}_2$ subgroup. The anomalies are determined by the consistency condition --- based on the Dai-Freed theorem --- of formulating a chiral fermion theory on a generic spacetime manifold with a structure associated with either one of the above symmetry groups and are represented by elements of some finite ab…

The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes

We review and extend high energy string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s-t and t-u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one leading trojectory string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in ter…

Deconfined criticality in the QED$_{3}$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited

The critical properties of the QED$_{3}$ Gross-Neveu-Yukawa (GNY) model in 2+1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the Néel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $ε$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inc…

Multikink scattering in the $ϕ^6$ model revisited

Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $ϕ^6$ model exhibit resonant scattering although the $ϕ^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\bar{\rm K} $$ {\rm K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\bar{\rm K} $$ {\rm K}$ scattering based on this collective bound mode trapped between the $\bar{\rm K} $$ {…

The Schwinger mechanism revisited

The vacuum persistence probability, $P_{vac}(t)$, for a system of charged fermions in a fixed, external, and spatially homogeneous electric field, was derived long ago by Schwinger; $w = -log[P_{vac}(t)]/ (V t)$ has often been identified as the rate at which fermion-antifermion pairs are produced per unit volume due to the electric field. In this paper, we separately compute exact expressions for both $w$ and for the rate of fermion-antifermion pair production per unit volume, $Γ$, and show that they differ. While $w$ is given by the standard Schwinger mechanism result $w$, an infinite series,…

Critical points of 2d disordered Dirac fermions: the Quantum Hall Transitions revisited

We propose a resolution of the renormalization group flow for the disordered Dirac fermion theories describing the quantum Hall transition (QHT) and spin Quantum Hall transition (SQHT), which previously revealed no perturbative fixed points at 1-loop and higher. The approach involves carrying out the flow in 2 stages, the first stage utilizing a new form of super spin-charge separation to flow to gl(1|1)_N and osp(2|2)_{-2N} supercurrent algebra theories, where N is the number of copies. This leads to the unconventional feature that at the critical point the exponents depend on the original nu…

Critical Boundary Sine-Gordon Revisited

We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a boundary mass term originally suggested in ref.[22]. We find that the entire SL(2,C) family of boundary states of a single boson are boundary sine-Gordon states and we derive a simple explicit expression for the boundary state in fermion variables and as a function of sine-Gordon coupling constants. We use this expression to compute the partition function. We obser…

The Axial Anomaly Revisited

We consider theories with gauged chiral fermions in which there are abelian anomalies, and no nonabelian anomalies (but there may be nonabelian gauge fields present). We construct an associated theory that is gauge-invariant, renormalizable, and with the same particle content, by adding a finite number of terms to the action. Alternatively one can view the new theory as arising from the original theory by using another regularization, one that is gauge-invariant. The situation is reminiscent of the mechanism of adding Fadeev-Popov ghosts to an unsatisfactory gauge theory, to arrive at the usua…

Gravitational Couplings on D-brane Revisited

Gravitational couplings in bulk space-time include those terms which are fixed by scattering amplitude of strings and ambiguous terms that are coming from the field redefinitions. These field redefinitions can be fixed in the bulk by ghost-free condition. In this paper we have revised the effective gravitational couplings on D-branes by including the field redefinitions. We find the gravitational effective action up to $α'^2$-order.

Witten index in supersymmetric 3d theories revisited

We have performed a direct calculation of Witten index in N = 1,2,3 supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework of Born-Oppenheimer (BO) approach by putting the system into a small spatial box and studying the effective Hamiltonian depending on the zero field harmonics. At the tree level, our results coincide with the results of Witten, but there is a difference in the way the loop effects are implemented. In Witten's approach, one has only take into account the fermion loops, which bring about a negative shift of the (chosen positive at the tree level) Chern-…

Strings in Plane Wave Backgrounds Revisited

String theory in an exact plane wave background is explored. A new example of singularity in the sense of string theory for nonsingular spacetime metric is presented. The 4-tachyon scattering amplitude is constructed. The spectrum of states found from the poles in the factorization turns out to be equivalent to that of the theory in flat space-time. The massless vertex operator is obtained from the residue of the first order pole.

Infrared Divergences in QED, Revisited

Recently it has been shown that the vacuum state in QED is infinitely degenerate. Moreover a transition among the degenerate vacua is induced in any nontrivial scattering process and determined from the associated soft factor. Conventional computations of scattering amplitudes in QED do not account for this vacuum degeneracy and therefore always give zero. This vanishing of all conventional QED amplitudes is usually attributed to infrared divergences. Here we show that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite. Our construc…

Open M-branes on AdS_{4/7} x S^{7/4} Revisited

We proceed further with a study of open supermembrane on the AdS_{4/7} x S^{7/4} backgrounds. Open supermembrane can have M5-brane and 9-brane as Dirichlet branes. In AdS and pp-wave cases the configurations of Dirichlet branes are restricted. A classification of possible Dirichlet branes, which is given up to and including the fourth order of fermionic variable þin hep-th/0310035, is shown to be valid even at full order of þ. We also discuss open M5-brane on the AdS_{4/7} x S^{7/4}.

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.

The Causal Perturbation Expansion Revisited: Rescaling the Interacting Dirac Sea

The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is in general not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the…

Ghost Systems Revisited: Modified Virasoro Generators and Logarithmic Conformal Field Theories

We study the possibility of extending ghost systems with higher spin to a logarithmic conformal field theory. In particular we are interested in c=-26 which turns out to behave very differently to the already known c=-2 case. The energy momentum tensor cannot be built anymore by a combination of derivatives of generalized symplectic fermion fields. Moreover, the logarithmically extended theory is only consistent when considered on nontrivial Riemann surfaces. This results in a LCFT with some unexpected properties. For instance the Virasoro mode L_0 is diagonal and for certain values of the def…

通过熵流分析重新审视具有一般转动的相对论自旋流体力学

Relativistic spin hydrodynamics revisited with general rotation by entropy-current analysis

本研究通过熵流分析重新审视含一般热涡度的狄拉克费米子相对论自旋流体力学正则表述，推导满足熵原理的本构关系，建立正则与唯象表述的伪规范变换联系，并通过线性模式分析发现两种表述的模式在梯度二阶下存在差异。