Variational principle, characteristic electric multipoles, and higher polarizing moments in field theory

1999 ◽  
Vol 119 (3) ◽  
pp. 750-760
Author(s):  
V. P. Kazantsev
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electric Multipoles

Unified Field Theory

1950 ◽  
Vol 2 ◽  
pp. 427-439 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Electromagnetic Fields ◽  
Linear Connection ◽  
Hamiltonian Function ◽  
Unified Theory ◽  
Unified Field Theory ◽  
Field Equations ◽  
Unified Field

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written(0.1)(0.2)(0.3)(0.4)

Quantum field theory

1955 ◽  
Vol 231 (1186) ◽  
pp. 321-335 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Variational Principle ◽  
Schrodinger Equation ◽  
Classical Field Theory ◽  
Functional Expression ◽  
Scattering Matrix ◽  
Classical Field ◽  
Quantum Field ◽  
Relativistic Analogue

A functional expression resembling the scattering matrix is introduced into classical field theory, and with this foundation a postulate of quantization is introduced analogous to the definitions of Feynmann. From this are derived some alternative and more familiar forms of field theory. A variational principle is introduced which provides a relativistic analogue of the familiar non-relativistie variational principle for the Schrödinger equation.

scholarly journals Real-time gravitational replicas: formalism and a variational principle

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Sean Colin-Ellerin ◽  
Xi Dong ◽  
Donald Marolf ◽  
Mukund Rangamani ◽  
Zhencheng Wang
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Analytic Continuation ◽  
Real Time ◽  
Path Integral ◽  
General Structure ◽  
Saddle Points ◽  
Analytic Boundary ◽  
Real Contour

Abstract This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called ‘splitting surface’. This feature is an important hallmark of unitarity in a field theory dual.

Time-Dependent Variational Principle for φ4 Field Theory

1995 ◽  
Vol 241 (1) ◽  
pp. 185-211 ◽  
Author(s):  
A.K. Kerman ◽  
C.Y. Lin
Keyword(s):  
Field Theory ◽  
Variational Principle ◽  
Time Dependent
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