scholarly journals SYMPLECTIC MATRIX, GAUGE INVARIANCE AND DIRAC BRACKETS FOR SUPER-QED

1999 ◽  
Vol 14 (29) ◽  
pp. 4687-4704
Author(s):  
D. T. ALVES ◽  
E. S. CHEB-TERRAB
Keyword(s):  
Gauge Invariance ◽  
Zero Mode ◽  
Matrix Approach ◽  
Supersymmetric Extension ◽  
Gauge Transformations ◽  
Symplectic Matrix ◽  
Dirac Brackets

The calculation of Dirac brackets (DB) using a symplectic matrix approach but in a Hamiltonian framework is discussed, and the calculation of the DB for the supersymmetric extension of QED (super-QED) is shown. The relation between the zero-mode of the pre-symplectic matrix and the gauge transformations admitted by the model is verified. A general prescription to construct Lagrangians linear in the velocities is also presented.

scholarly journals Extracting topological information from momentum space propagators

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Fabrizio Canfora ◽  
David Dudal ◽  
Alex Giacomini ◽  
Igor F. Justo ◽  
Pablo Pais ◽  
...  
Keyword(s):  
Gauge Invariance ◽  
Momentum Space ◽  
Chiral Symmetry Breaking ◽  
Topological Invariant ◽  
Analytic Structure ◽  
Topological Information ◽  
Gauge Transformations ◽  
Small Gauge ◽  
Topological Number

Abstract A new topological invariant quantity, sensitive to the analytic structure of both fermionic and bosonic propagators, is proposed. The gauge invariance of our construct is guaranteed for at least small gauge transformations. A generalization compatible with the presence of complex poles is introduced and applied to the classification of propagators typically emerging from non-perturbative considerations. We present partial evidence that the topological number can be used to detect chiral symmetry breaking or deconfinement.

scholarly journals Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond

1997 ◽  
Vol 14 (9) ◽  
pp. 2585-2606 ◽  
Author(s):  
Marco Bruni ◽  
Sabino Matarrese ◽  
Silvia Mollerach ◽  
Sebastiano Sonego
Keyword(s):  
Gauge Invariance ◽  
Second Order ◽  
Gauge Transformations

scholarly journals DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM

2007 ◽  
Vol 22 (21) ◽  
pp. 3605-3620 ◽  
Author(s):  
E. M. C. ABREU ◽  
A. C. R. MENDES ◽  
C. NEVES ◽  
W. OLIVEIRA ◽  
F. I. TAKAKURA
Keyword(s):  
Phase Space ◽  
Gauge Invariance ◽  
Zero Mode ◽  
Mass Term ◽  
Gauge Invariant ◽  
Embedding Method ◽  
Symplectic Embedding ◽  
The One ◽  
Topological Term

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

scholarly journals One-loop structure of parton distribution for the gluon condensate and “zero modes”

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Anatoly Radyushkin ◽  
Shuai Zhao
Keyword(s):  
Gauge Invariance ◽  
Parton Distribution ◽  
Light Cone ◽  
Zero Mode ◽  
Gluon Condensate ◽  
Loop Structure ◽  
Matrix Elements ◽  
Zero Modes ◽  
Strict Compliance ◽  
Evolution Kernel

Abstract We present results for one-loop corrections to the recently introduced “gluon condensate” PDF F(x). In particular, we give expression for the gg-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No “zero mode” δ(x) terms were found for the twist-4 gluon PDF F(x). However a q2δ(x) term was found for the ξ = 0 GPD F(x, q2) at nonzero momentum transfer q. Overall, our results do not agree with the original attempt of one-loop calculations of F(x) for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.

scholarly journals Lorentz breaking and SU(2)L × U(1)Y gauge invariance for neutrinos

2019 ◽  
Vol 28 (09) ◽  
pp. 1950072 ◽  
Author(s):  
U. D. Jentschura ◽  
I. Nándori ◽  
G. Somogyi
Keyword(s):  
Gauge Invariance ◽  
Effective Interaction ◽  
Lorentz Violation ◽  
Research Area ◽  
Cerenkov Radiation ◽  
General Interest ◽  
Gauge Transformations ◽  
Neutrino Sector ◽  
Neutrino Pair ◽  
Charged Leptons

Conceivable Lorentz-violating effects in the neutrino sector remain a research area of great general interest, as they touch upon the very foundations on which the Standard Model and our general understanding of fundamental interactions are laid. Here, we investigate the relation of Lorentz violation in the neutrino sector in light of the fact that neutrinos and the corresponding left-handed charged leptons form [Formula: see text] doublets under the electroweak gauge group. Lorentz-violating effects thus cannot be fully separated from questions related to gauge invariance. The model dependence of the effective interaction Lagrangians used in various recent investigations is explored with a special emphasis on neutrino splitting, otherwise known as the neutrino-pair Cerenkov radiation and vacuum-pair emission (electron–positron-pair Cerenkov radiation). We highlight two scenarios in which Lorentz-violating effects do not necessarily also break electroweak gauge invariance. The first of these involves a restricted set of gauge transformations, a subgroup of [Formula: see text], while in the second where differential Lorentz violation is exclusively introduced by the mixing of the neutrino flavor and mass eigenstates. Our study culminates in a model which fully preserves [Formula: see text] gauge invariance, involves flavor-dependent Lorentz-breaking parameters, and still allows for Cerenkov-type decays to proceed.

THE EXTRA GAUGE SYMMETRY OF STRING DEFORMATIONS IN ELECTROMAGNETISM WITH CHARGES AND DIRAC MONOPOLES

1992 ◽  
Vol 07 (19) ◽  
pp. 4693-4705 ◽  
Author(s):  
H. KLEINERT
Keyword(s):  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Quantum Physics ◽  
Magnetic Monopoles ◽  
Quantization Condition ◽  
Gauge Transformations ◽  
Charge Quantization ◽  
Particle Orbits ◽  
Local Gauge Invariance ◽  
Physical Consequences

We point out that electromagnetism with Dirac magnetic monopoles harbors an extra local gauge invariance called monopole gauge invariance. The gauge transformations act on a gauge field of monopoles [Formula: see text] and are independent of the ordinary electromagnetic gauge invariance. The extra invariance expresses the physical irrelevance of the shape of the Dirac strings attached to the monopoles. The independent nature of the new gauge symmetry is illustrated by comparison with two other systems, superfluids and solids, which are not gauge-invariant from the outset but which nevertheless possess a precise analog of the monopole gauge invariance in their vortex and defect structure, respectively. The extra monopole gauge invariance is shown to be responsible for the Dirac charge quantization condition 2eg/ħc=integer, which can now be proved for any fixed particle orbits, i.e. without invoking fluctuating orbits which would correspond to the standard derivation using Schrödinger wave functions. The only place where quantum physics enters in our theory is by admitting the action to jump by 2πħ×integer without physical consequences when moving the string at fixed particle orbits.

scholarly journals Hamiltonian dynamics of 5D Kalb–Ramond theories with a compact extra dimension

2015 ◽  
Vol 12 (04) ◽  
pp. 1550039 ◽  
Author(s):  
Alberto Escalante ◽  
A. López-Villanueva
Keyword(s):  
Extra Dimension ◽  
Hamiltonian Dynamics ◽  
Gauge Transformations ◽  
Constraint Program ◽  
Goldstone Bosons ◽  
Compact Dimension ◽  
Dirac Brackets ◽  
Hamiltonian Analysis

A detailed Hamiltonian analysis for a 5D Kalb–Ramond, massive Kalb–Ramond and Stüeckelberg Kalb–Ramond theories with an extra compact dimension is performed. We develop a complete constraint program, then we quantize the theory by constructing the Dirac brackets. From the gauge transformations of the theories, we fix a particular gauge and we find pseudo-Goldstone bosons in Kalb–Ramond and Stüeckelberg Kalb–Ramond systems. Finally we discuss some remarks and prospects.

scholarly journals LOOP VARIABLES AND GAUGE INVARIANCE IN (OPEN) BOSONIC STRING THEORY

2002 ◽  
Vol 17 (18) ◽  
pp. 1175-1190 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
String Theory ◽  
Gauge Invariance ◽  
Equations Of Motion ◽  
Standard Form ◽  
Open String ◽  
Finite Width ◽  
Massive Mode ◽  
Gauge Transformations ◽  
Variable Approach ◽  
Free Case

We give a simplified and more complete description of the loop variable approach for writing down gauge-invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite worldsheet cutoff and that in the ir limit, equivalence with the Callan–Symanzik β-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon–photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite worldsheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into the standard form.

scholarly journals A PEDAGOGICAL INTRODUCTION TO THE SLAVNOV FORMULATION OF QUANTUM YANG–MILLS THEORY

2011 ◽  
Vol 08 (04) ◽  
pp. 821-834
Author(s):  
HOSSEIN GHORBANI ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Quantum Gravity ◽  
Gauge Invariance ◽  
Lorentz Invariance ◽  
Functional Integral ◽  
Coulomb Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
S Matrix ◽  
Ghost Field

Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

scholarly journals THE PROTON SPIN DECOMPOSITION: PATH DEPENDENCE AND GAUGE SYMMETRY

2014 ◽  
Vol 25 ◽  
pp. 1460030 ◽  
Author(s):  
CÉDRIC LORCÉ
Keyword(s):  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Path Dependence ◽  
Proton Spin ◽  
Gauge Potential ◽  
Gauge Transformations ◽  
Different Types ◽  
Decomposition Path

We discuss the different types of decomposition of the proton spin. We stress that, despite their lack of uniqueness, the Chen et al. and Wakamatsu decompositions are perfectly measurable. We argue that a large part of the recent controversies boils down to the fact that there actually exist two types of gauge transformations in the Chen et al. approach, where physical and gauge degrees of freedom of the gauge potential are explicitly separated. By carefully distinguishing these two types of gauge transformations, one can easily understand how the concepts of gauge invariance, Stueckelberg symmetry, path dependence and measurability are linked to each other.

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