Novel Use of Legendre Transformation in Field Theory and Many Particle Systems

1995 ◽  
Vol 121 ◽  
pp. 1-428 ◽  
Author(s):  
Reijiro Fukuda ◽  
Masahiro Komachiya ◽  
Satoshi Yokojima ◽  
Yoko Suzuki ◽  
Ko Okumura ◽  
...  
Keyword(s):  
Field Theory ◽  
Particle Systems ◽  
Legendre Transformation

scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

Fluctuation theory for systems of signed and unsigned particles with interaction mechanisms based on intersection local times

1989 ◽  
Vol 21 (2) ◽  
pp. 334-356 ◽  
Author(s):  
Robert J. Adler
Keyword(s):  
Field Theory ◽  
Interaction Mechanism ◽  
Particle Systems ◽  
Fluctuation Theory ◽  
Local Times ◽  
Quantum Field ◽  
First Case ◽  
Infinite Collection ◽  
Euclidean Quantum Field Theory ◽  
Intersection Local Times

We consider two distinct models of particle systems. In the first we have an infinite collection of identical Markov processes starting at random throughout Euclidean space. In the second a random sign is associated with each process. An interaction mechanism is introduced in each case via intersection local times, and the fluctuation theory of the systems studied as the processes become dense in space. In the first case the fluctuation theory always turns out to be Gaussian, regardless of the order of the intersections taken to introduce the interaction mechanism. In the second case, an interaction mechanism based on kth order intersections leads to a fluctuation theory akin to a :φ k: Euclidean quantum field theory. We consider the consequences of these results and relate them to different models previously studied in the literature.

scholarly journals Interparticle potentials in a scalar quantum field theory with a Higgs-like mediating field

2013 ◽  
Vol 91 (4) ◽  
pp. 279-292 ◽  
Author(s):  
Alexander Chigodaev ◽  
Jurij W. Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Equations ◽  
Hamiltonian Formalism ◽  
Particle Systems ◽  
Stationary States ◽  
Quantum Field ◽  
Scalar Theory ◽  
Scalar Quantum ◽  
Interparticle Potentials

We study the interparticle potentials for few-particle systems in a scalar theory with a nonlinear mediating field of the Higgs type. We use the variational method, in a reformulated Hamiltonian formalism of quantum field theory, to derive relativistic three- and four-particle wave equations for stationary states of these systems. We show that the cubic and quartic nonlinear terms modify the attractive Yukawa potentials but do not change the attractive nature of the interaction if the mediating fields are massive.

Fluctuation theory for systems of signed and unsigned particles with interaction mechanisms based on intersection local times

1989 ◽  
Vol 21 (02) ◽  
pp. 334-356
Author(s):  
Robert J. Adler
Keyword(s):  
Field Theory ◽  
Interaction Mechanism ◽  
Particle Systems ◽  
Fluctuation Theory ◽  
Local Times ◽  
Quantum Field ◽  
First Case ◽  
Infinite Collection ◽  
Euclidean Quantum Field Theory ◽  
Intersection Local Times

We consider two distinct models of particle systems. In the first we have an infinite collection of identical Markov processes starting at random throughout Euclidean space. In the second a random sign is associated with each process. An interaction mechanism is introduced in each case via intersection local times, and the fluctuation theory of the systems studied as the processes become dense in space. In the first case the fluctuation theory always turns out to be Gaussian, regardless of the order of the intersections taken to introduce the interaction mechanism. In the second case, an interaction mechanism based onkth order intersections leads to a fluctuation theory akin to a :φk: Euclidean quantum field theory. We consider the consequences of these results and relate them to different models previously studied in the literature.

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