A Lagrangian formalism for the Einstein–Yang–Mills equations

1995 ◽  
Vol 36 (7) ◽  
pp. 3733-3742 ◽  
Author(s):  
D. C. Robinson
Keyword(s):  
Lagrangian Formalism ◽  
Yang Mills

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

scholarly journals Field-dependent BRST–anti-BRST Lagrangian transformations

2015 ◽  
Vol 30 (04n05) ◽  
pp. 1550021 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Symmetry Breaking ◽  
Ward Identity ◽  
Brst Symmetry ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Change Of Variables ◽  
Field Dependent ◽  
Renormalization Group Approach ◽  
Quantum Action

We continue our study of finite BRST–anti-BRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790 [hep-th] and arXiv:1406.0179 [hep-th]], with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters, and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179 [hep-th]], which corresponds to a change of variables with functionally dependent parameters λa = UaΛ induced by a finite Bosonic functional Λ(ϕ, π, λ) and by the anticommuting generators Ua of BRST–anti-BRST transformations in the space of fields ϕ and auxiliary variables πa, λ. We obtain a Ward identity depending on the field-dependent parameters λa and study the problem of gauge dependence, including the case of Yang–Mills theories. We examine a formulation with BRST–anti-BRST symmetry breaking terms, additively introduced into the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST–anti-BRST settings. These concepts are applied to the average effective action in Yang–Mills theories within the functional renormalization group approach.

scholarly journals Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians

2003 ◽  
Vol 18 (31) ◽  
pp. 2207-2216
Author(s):  
Rajsekhar Bhattacharyya ◽  
Debashis Gangopadhyay
Keyword(s):  
Classical Solution ◽  
Electric Charge ◽  
Higgs Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Lagrangian Formalism ◽  
Expectation Value ◽  
Yang Mills ◽  
Noncommuting Coordinates

The spacetime dependent Lagrangian formalism of Refs. 1 and 2 is used to obtain a classical solution of Yang–Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field viz. ϕa = A/e, where A is a constant and e is the Yang–Mills coupling (related to the usual electric charge). The solution can also accommodate noncommuting coordinates on the boundary of the theory which may be used to construct D-brane actions. The formalism is also used to obtain the Deser–Gomberoff–Henneaux–Teitelboim results10 for dyon charge quantisation in Abelian p-form theories in dimensions D = 2(p+1) for both even and odd p.

Efficient Treatment of Fixed and Induced Dipolar Interactions

2000 ◽  
Vol 653 ◽  
Author(s):  
Celeste Sagui ◽  
Thoma Darden
Keyword(s):  
Molecular Dynamics ◽  
Md Simulations ◽  
Lagrangian Formalism ◽  
Dipolar Interactions ◽  
Time Step ◽  
Efficient Treatment ◽  
Particle Mesh Ewald ◽  
Fixed Charges ◽  
Self Consistency ◽  
Induced Dipoles

AbstractFixed and induced point dipoles have been implemented in the Ewald and Particle-Mesh Ewald (PME) formalisms. During molecular dynamics (MD) the induced dipoles can be propagated along with the atomic positions either by interation to self-consistency at each time step, or by a Car-Parrinello (CP) technique using an extended Lagrangian formalism. The use of PME for electrostatics of fixed charges and induced dipoles together with a CP treatment of dipole propagation in MD simulations leads to a cost overhead of only 33% above that of MD simulations using standard PME with fixed charges, allowing the study of polarizability in largemacromolecular systems.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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