scholarly journals Large gauge transformation, soft theorem, and Infrared divergence in inflationary spacetime

2017 ◽  
Vol 2017 (10) ◽  
Author(s):  
Takahiro Tanaka ◽  
Yuko Urakawa
Keyword(s):  
Gauge Transformation ◽  
Infrared Divergence ◽  
Large Gauge Transformation

scholarly journals Asymptotic Weyl double copy

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Hadi Godazgar ◽  
Mahdi Godazgar ◽  
Ricardo Monteiro ◽  
David Peinador Veiga ◽  
C. N. Pope
Keyword(s):  
Black Holes ◽  
Gauge Transformation ◽  
Single Copy ◽  
Characteristic Value ◽  
Full Solution ◽  
Double Copy ◽  
Asymptotic Formulation ◽  
Large Gauge Transformation ◽  
Asymptotic Symmetries

Abstract A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a large gauge transformation.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

scholarly journals LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

2001 ◽  
Vol 16 (10) ◽  
pp. 1679-1701 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Gauge Transformation ◽  
Dimensional Reduction ◽  
Mass Shell ◽  
Bosonic String ◽  
Higher Dimension ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

scholarly journals INFRARED DIVERGENCE IN QED3 AT FINITE TEMPERATURE

1999 ◽  
Vol 14 (18) ◽  
pp. 2921-2947 ◽  
Author(s):  
DOMINIC LEE ◽  
GEORGIOS METIKAS
Keyword(s):  
Finite Temperature ◽  
Statistical Physics ◽  
Order Term ◽  
Dyson Equation ◽  
Infrared Divergence ◽  
Fermion Mass ◽  
Photon Propagator ◽  
Transverse Part ◽  
Transverse Photon ◽  
Range Of Values

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour QED 3 at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artifact of taking into account only the leading order term in the [Formula: see text] expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger–Dyson equation, we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio r=2* Mass (T=0)/critical temperature is approximately 6, consistent with previous calculations which neglected the transverse photon contribution.

scholarly journals All-loop-orders relation between Regge limits of $$ \mathcal{N} $$ = 4 SYM and $$ \mathcal{N} $$ = 8 supergravity four-point amplitudes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Stephen G. Naculich
Keyword(s):  
Infrared Divergence ◽  
Loop Order ◽  
Loop Correction ◽  
Divergence Structure ◽  
Regge Limit ◽  
Point Amplitude

Abstract We examine in detail the structure of the Regge limit of the (nonplanar) $$ \mathcal{N} $$ N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through $$ \mathcal{O}\left({\upepsilon}^2\right) $$ O ϵ 2 at two loops, and through $$ \mathcal{O}\left({\upepsilon}^0\right) $$ O ϵ 0 at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the $$ \mathcal{N} $$ N = 8 supergravity four-point amplitude.

Smoothness of the action of the gauge transformation group on connections

1986 ◽  
Vol 27 (10) ◽  
pp. 2469-2474 ◽  
Author(s):  
M. C. Abbati ◽  
R. Cirelli ◽  
A. Manià ◽  
P. Michor
Keyword(s):  
Gauge Transformation ◽  
Transformation Group

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

Chiral bosonic field theories and the quantum Hall effect

2001 ◽  
Vol 79 (9) ◽  
pp. 1121-1131 ◽  
Author(s):  
P Bracken
Keyword(s):  
Hall Effect ◽  
Gauge Transformation ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Equation Of Motion ◽  
Hall Conductivity ◽  
Field Theories ◽  
Bosonic Field ◽  
Chern Simons

The gauge-transformation properties of the actions of certain scalar and Chern–Simons theories are investigated, including contributions from the boundary. By imposing chirality constraints on the fields, these types of theories can be used to describe the quantum Hall effect. It is shown that the corresponding equation of motion for the associated current for the theory generates an anomaly, which can be related directly to the Hall conductivity. PACS Nos.: 73.43, 03.70, 11.10, 11.30R

scholarly journals COVARIANT DESCRIPTION OF PARAMETRIZED NONRELATIVISTIC HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (15) ◽  
pp. 2473-2493 ◽  
Author(s):  
MAURICIO MONDRAGÓN ◽  
MERCED MONTESINOS
Keyword(s):  
Phase Space ◽  
Gauge Transformation ◽  
Hamiltonian Systems ◽  
Symplectic Structure ◽  
Canonical Formalism ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Algebra Of Observables ◽  
Covariant Description ◽  
Constraint Surface

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

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