Phase structure of the scalar Yukawa model with compactified spatial dimensions

2016 ◽  
Vol 31 (20) ◽  
pp. 1650121 ◽  
Author(s):  
L. M. Abreu ◽  
A. P. C. Malbouisson ◽  
E. S. Nery
Keyword(s):  
Field Theory ◽  
Phase Structure ◽  
Vector Fields ◽  
Boundary Effects ◽  
Quantum Field ◽  
Yukawa Model ◽  
Complex Scalar ◽  
Scalar And Vector Fields ◽  
Spatial Dimensions ◽  
Complex Scalar Field

In this work, we investigate the thermodynamic behavior of the generalized scalar Yukawa model, composed of a complex scalar field interacting with real scalar and vector fields. In particular, boundary effects on the phase structure are discussed using methods of quantum field theory on toroidal topologies. We concentrate on the dependence of the thermodynamics with the number of compactified spatial dimensions. In this sense, the phase transitions are analyzed and compared with the system in the situations of one, two and three compactified spatial dimensions. Our findings suggest that the presence of more boundaries tends to inhibit the broken phase.

Phase structure of a Yukawa-like model in the presence of magnetic background and boundaries

2016 ◽  
Vol 31 (23) ◽  
pp. 1650128 ◽  
Author(s):  
L. M. Abreu ◽  
E. S. Nery
Keyword(s):  
Magnetic Field ◽  
Phase Structure ◽  
Vector Fields ◽  
Strong Dependence ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Complex Scalar ◽  
Scalar And Vector Fields ◽  
Complex Scalar Field

In this paper, we investigate the thermodynamics of a Yukawa-like model, constituted of a complex scalar field interacting with real scalar and vector fields, in the presence of an external magnetic field and boundaries. By making use of mean-field approximation, we analyze the phase structure of this model at effective chemical equilibrium, under change of values of the relevant parameters of the model, focusing on the influence of the boundaries on the phase structure. The findings reveal a strong dependence of the nature of the phase structure on temperature, magnetic background and size of compactified coordinate, with possibility of a two-step phase transition.

scholarly journals Some boundary effects in quantum field theory

2004 ◽  
Vol 70 (6) ◽  
Author(s):  
V. B. Bezerra ◽  
M. A. Rego-Monteiro
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Effects ◽  
Quantum Field

Field models

2021 ◽  
pp. 42-69
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Electromagnetic Field ◽  
Scalar Field ◽  
Spinor Field ◽  
Vector Fields ◽  
Sigma Model ◽  
Complex Scalar ◽  
Yang Mills ◽  
Scalar Field Models ◽  
Complex Scalar Field ◽  
Mills Field

This chapter provides constructions of Lagrangians for various field models and discusses the basic properties of these models. Concrete examples of field models are constructed, including real and complex scalar field models, the sigma model, spinor field models and models of massless and massive free vector fields. In addition, the chapter discusses various interactions between fields, including the interactions of scalars and spinors with the electromagnetic field. A detailed discussion of the Yang-Mills field is given as well.

scholarly journals Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Parijat Banerjee ◽  
Adwait Gaikwad ◽  
Anurag Kaushal ◽  
Gautam Mandal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Cold Atom ◽  
Quantum Field ◽  
Approach To Equilibrium ◽  
Zero Mass ◽  
Quantum Quench ◽  
Spatial Dimensions ◽  
Arbitrary Dimensions

Abstract In many quantum quench experiments involving cold atom systems the post-quench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N ) models.

Boundary effects in quantum field theory

1979 ◽  
Vol 20 (12) ◽  
pp. 3063-3080 ◽  
Author(s):  
D. Deutsch ◽  
P. Candelas
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Effects ◽  
Quantum Field

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals Generative Model Study for 1+1d-Complex Scalar Field Theory

2021 ◽  
Author(s):  
Kai Zhou ◽  
Gergely Endrodi ◽  
Long-Gang Pang ◽  
Horst Stoecker
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Generative Model ◽  
Scalar Field Theory ◽  
Complex Scalar ◽  
Model Study ◽  
Complex Scalar Field ◽  
1D Complex

scholarly journals Field theory in normal conical coordinates

2021 ◽  
Vol 244 ◽  
pp. 09004
Author(s):  
Dmitry Nesnov
Keyword(s):  
Field Theory ◽  
Vector Field ◽  
Computer Graphics ◽  
Vector Fields ◽  
Complex Structure ◽  
Curvilinear Coordinates ◽  
Mathematical Apparatus ◽  
Spherical Coordinate ◽  
Geometrical Modeling ◽  
Scalar And Vector Fields

In the scientific literature, the field theory is most fully covered in the cylindrical and spherical coordinate systems. This is explained by the fact that the mathematical apparatus of these systems is most well studied. When the source of field has a more complex structure than a point or a straight line, there is a need for new approaches to their study. The goal of this research is to adapt the field theory related to curvilinear coordinates in order to represent it in the normal conical coordinates. In addition, an important part of the research is the development of a geometrical modeling apparatus for scalar and vector field level surfaces using computer graphics. The paper shows the dependences of normal conical coordinates on rectangular Cartesian coordinates, Lame coefficients. The differential characteristics of the scalar and vector fields in normal conical coordinates are obtained: Laplacian of scalar and vector fields, divergence, rotation of the vector field. The example case shows the features of the application of the mathematical apparatus of geometrical field modeling in normal conical coordinates. For the first time, expressions for the characteristics of the scalar and vector fields in normal conical coordinates are obtained. Methods for geometrical modeling of fields using computer graphics have been developed to provide illustration in their study.

scholarly journals Field theory in normal toroidal coordinates

2018 ◽  
Vol 193 ◽  
pp. 03022
Author(s):  
Dmitry V. Nesnov
Keyword(s):  
Field Theory ◽  
Vector Field ◽  
Computer Graphics ◽  
Geometric Modeling ◽  
Vector Fields ◽  
Scientific Paper ◽  
Curvilinear Coordinates ◽  
Coordinate Systems ◽  
Scalar And Vector Fields ◽  
Toroidal Coordinates

Field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems has been thoroughly studied. Sources of field with more complex structures require new approaches to their study. The purpose of this research is to adapt the field theory referred to curvilinear coordinates and represent it in normal toroidal coordinates. Another purpose is to develop the foundations of geometric modeling with the use of computer graphics for visualizing the level surfaces. The dependence of normal toroidal coordinates on rectangular Cartesian coordinates and Lame coefficients is shown in this scientific paper. Differential characteristics of scalar and vector fields in normal toroidal coordinates are obtained: scalar and vector field laplacians, divergence, and rotation of vector field. The example shows the technique of modeling the field and its further computer visualization. The technique of reading the internal equation of the surface is presented and the influence of the values of the parameters on the shape of the surface is shown. For the first time, expressions of scalar and vector field characteristics in normal toroidal coordinates are obtained, the fundamentals of geometric modeling of fields with the use of computer graphics tools are developed for the purpose of providing visibility for their study.

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