Related papers: Group projection method in statistical systems
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be…
In this paper, the relationships between Lie symmetry groups and fundamental solutions for a class of conformable time fractional partial differential equations (PDEs) with variable coefficients are investigated. Specifically, the…
We review some aspects of the use of a technique known as group averaging, which provides a tool for the study of constrained systems. We focus our attention on the case where the gauge group is non-compact, and a `renormalized' group…
In the context of supersymmetric quantum mechanics we formulate new supersymmetric localization principle, with application to trace formulas for a full thermal partition function. Unlike the standard localization principle, this new…
A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…
We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a…
Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we…
In this contribution we give an introduction to the foundations and methods of lattice gauge theory. Starting with a brief discussion of the quantum mechanical path integral, we develop the main ingredients of lattice field theory:…
The design and implementation of large sets of spatially extended baryon operators for use in lattice simulations are described. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the…
We introduce new techniques for calculations in Gauge theories with extended supersymmetry. We are working in Projective Superspace where the $SU(2)$ R-symmetry is realized geometrically by including an auxilliary $\mathbb{CP}^1$ component…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
A method is presented which allows one to introduce collective coordinates self-consistently, in distinction to the Caldeira-Leggett model. It is demonstrated how the partition function Z for the total nuclear system can be calculated to…
It is proposed to use the Lie group theory of symmetries of differential equations to investigate the system of equations describing a static star in a radiative and convective equilibrium. It is shown that the action of an admissible group…
A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early universe and in particle colliders, starting from the Standard Model. Classical-computing methods, via the framework of…
Reductive (or semisimple) algebraic groups, Lie groups and Lie algebras have a rich geometry determined by their parabolic subgroups and subalgebras, which carry the structure of a building in the sense of J. Tits. We present herein an…
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential.…
We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach…
We write the partition function for a lattice gauge theory, with compact gauge group, exactly in terms of unconstrained variables and show that, in the mean field approximation, the dynamics of pure gauge theories, invariant under compact,…
Self-gravitating system are non-equilibrium a priory. A new approach is proposed, which employs a non-equilibrium statistical operator into account inhomogeneous distribution of particles and temperature. The method involves the saddle -…