Gauge invariance and canonical transformations in Dirac generalized mechanics

2005 ◽  
pp. 514-516
Author(s):  
Ricardo A. Tello Llanos
Keyword(s):  
Gauge Invariance ◽  
Canonical Transformations ◽  
Generalized Mechanics

Gauge invariance of Dirac’s generalized mechanics

1984 ◽  
Vol 40 (4) ◽  
pp. 115-120 ◽  
Author(s):  
R. A. Tello-Llanos
Keyword(s):  
Gauge Invariance ◽  
Generalized Mechanics

Hamiltonian Mechanics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Angular Momentum ◽  
Jacobi Equation ◽  
Modern Theory ◽  
Hamiltonian Mechanics ◽  
Lagrangian Mechanics ◽  
Canonical Transformations ◽  
Canonical Variables ◽  
Light Waves ◽  
Hamilton Jacobi Equation ◽  
Common Action

Hamilton’s genius was to understand what were the true variables of mechanics (the “p − q,” conjugate coordinates, or canonical variables), and this led to Hamilton’s Mechanics which could obtain qualitative answers to a wider ranger of problems than Lagrangian Mechanics. It is explained how Hamilton’s canonical equations arise, why the Hamiltonian is the “central conception of all modern theory” (quote of Schrödinger’s), what the “p − q” variables are, and what phase space is. It is also explained how the famous conservation theorems arise (for energy, linear momentum, and angular momentum), and the connection with symmetry. The Hamilton-Jacobi Equation is derived using infinitesimal canonical transformations (ICTs), and predicts wavefronts of “common action” spreading out in (configuration) space. An analogy can be made with geometrical optics and Huygen’s Principle for the spreading out of light waves. It is shown how Hamilton’s Mechanics can lead into quantum mechanics.

Poisson Brackets & Angular Momentum

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Generating Functions ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Poisson Brackets ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Gauge Transformations ◽  
The Third ◽  
Point Transformations ◽  
Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals All-plus helicity off-shell gauge invariant multigluon amplitudes at one loop

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Etienne Blanco ◽  
Andreas van Hameren ◽  
Piotr Kotko ◽  
Krzysztof Kutak
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Invariance ◽  
Arbitrary Number ◽  
Gauge Invariant

Abstract We calculate one loop scattering amplitudes for arbitrary number of positive helicity on-shell gluons and one off-shell gluon treated within the quasi-multi Regge kinematics. The result is fully gauge invariant and possesses the correct on-shell limit. Our method is based on embedding the off-shell process, together with contributions needed to retain gauge invariance, in a bigger fully on-shell process with auxiliary quark or gluon line.

scholarly journals Monopole fluctuation of the CMB and its gauge invariance

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Sandra Baumgartner ◽  
Jaiyul Yoo
Keyword(s):  
Gauge Invariance

GAUGE INVARIANCE AND CONSTRAINTS: OPEN GAUGE ALGEBRAS

1992 ◽  
Vol 07 (22) ◽  
pp. 5549-5561 ◽  
Author(s):  
KH. S. NIROV ◽  
P.N. PYATOV ◽  
A.V. RAZUMOV
Keyword(s):  
Wide Class ◽  
Gauge Invariance ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant

For a wide class of gauge-invariant systems with open gauge algebras the Hamiltonian description is constructed and the Poisson brackets of the constraints are calculated. It is shown that in the case under consideration there arise only first class constraints.

A quantization of the electromagnetic field

1983 ◽  
Vol 61 (8) ◽  
pp. 1172-1183
Author(s):  
Anton Z. Capri ◽  
Gebhard Grübl ◽  
Randy Kobes
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Gauge Invariance ◽  
Free Field ◽  
External Source ◽  
Field Level ◽  
Manifest Covariance ◽  
The One ◽  
Physical Spaces

Quantization of the electromagnetic field in a class of covariant gauges is performed on a positive metric Hilbert space. Although losing manifest covariance, we find at the free field level the existence of two physical spaces where Poincaré transformations are implemented unitarily. This gives rise to two different physical interpretations of the theory. Unitarity of the S operator for an interaction with an external source then forces one to postulate that a restricted gauge invariance must hold. This singles out one interpretation, the one where two transverse photons are physical.

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