scholarly journals Gauge independence in a higher-order Lagrangian formalism via change of variables in the path integral

2015 ◽  
Vol 742 ◽  
pp. 23-28 ◽  
Author(s):  
Igor A. Batalin ◽  
Klaus Bering
Keyword(s):  
Path Integral ◽  
Higher Order ◽  
Lagrangian Formalism ◽  
Change Of Variables ◽  
Higher Order Lagrangian

scholarly journals Second class constraints in a higher-order Lagrangian formalism

1997 ◽  
Vol 408 (1-4) ◽  
pp. 235-240 ◽  
Author(s):  
I.A. Batalin ◽  
K. Bering ◽  
P.H. Damgaard
Keyword(s):  
Higher Order ◽  
Lagrangian Formalism ◽  
Higher Order Lagrangian

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 COORDINATE-INVARIANT PATH INTEGRAL METHODS IN CONFORMAL FIELD THEORY

2006 ◽  
Vol 21 (17) ◽  
pp. 3525-3563 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Direct Calculation ◽  
Conformal Anomaly ◽  
Operator Formalism ◽  
Conformal Field ◽  
Integral Methods ◽  
Change Of Variables ◽  
Definition Of

We present a coordinate-invariant approach, based on a Pauli–Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy–momentum in the Pauli–Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding nontensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy–momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy–momentum two-point functions in our formalism.

scholarly journals Higher-order Lagrangian perturbative theory for the Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 119-120
Author(s):  
Takayuki Tatekawa ◽  
Shuntaro Mizuno
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Initial Conditions ◽  
Higher Order ◽  
Order Perturbation ◽  
Initial Condition ◽  
The Difference ◽  
Fifth Order ◽  
The Universe ◽  
Higher Order Lagrangian

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

scholarly journals A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics

2019 ◽  
Vol 353 ◽  
pp. 467-490 ◽  
Author(s):  
Evan J. Lieberman ◽  
Xiaodong Liu ◽  
Nathaniel R. Morgan ◽  
Darby J. Luscher ◽  
Donald E. Burton
Keyword(s):  
Discontinuous Galerkin ◽  
Higher Order ◽  
Hydrodynamic Method ◽  
Solid Dynamics ◽  
Higher Order Lagrangian
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