Related papers: Quantizing Yang-Mills Theory: From Parisi-Wu Stoch…
The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…
Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum…
Recently, gauge field theory approaches were extensively used in order to discuss the physical consequences of spin-orbit interactions in condensed matter physics. An SU(2)$\times$U(1) gauge theory is very naturally borne out and provides…
We give a new way of looking at the Cho--Faddeev--Niemi (CFN) decomposition of the Yang-Mills theory to answer how the enlarged local gauge symmetry respected by the CFN variables is restricted to obtain another Yang-Mills theory with the…
Wilson lines in gauge theories admit several path integral descriptions. The first one (due to Alekseev-Faddeev-Shatashvili) uses path integrals over coadjoint orbits. The second one (due to Diakonov-Petrov) replaces a 1-dimensional path…
It has been known for some time that there are many inequivalent quantizations possible when the configuration space of a system is a coset space G/H. Viewing this classical system as a constrained system on the group G, we show that these…
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this…
We discuss a quantization of the Yang--Mills theory with an internal symmetry group $SO(1,n)$ treated as a unified theory of all interactions. In one-loop calculations, we show that Einstein gravity can be considered as an approximation to…
The equations for Yang-Mills field in a medium are derived in a linear approximation with respect to the gauge coupling parameter and the external field. The obtained equations closely resemble the macroscopic Maxwell equations. A canonical…
For the spinning superparticle we construct the pull-back of the world-line path integral to super moduli space in the Hamiltonian formulation. We describe the underlying geometric decomposition of super moduli space. Algebraically, this…
Local solutions to the 3D stochastic quantisation equations of Yang-Mills-Higgs were constructed in (arXiv:2201.03487), and it was shown that, in the limit of smooth mollifications, there exists a mass renormalisation of the Yang-Mills…
We derive the quantization map in geometric quantization of symplectic manifolds via the Poisson sigma model. This gives a polarization-free (path integral) definition of quantization which pieces together most known quantization schemes.…
In the present work, multiplicative renormalization \cite{dixon} for Yang-Mills theories is reviewed. While this subject is not new, it is suggested that a clear understanding of these methods leads to a systematic way for interpreting the…
Relativistic generalization of Path Integral Monte-Carlo method has been proposed and some possible applications have been discussed.
In recent years, the effects of removing infinitesimal Gribov copies from the path integral of gauge-fixed Yang-Mills-Chern-Simons theories formulated in three-dimensional Euclidean space have been investigated. Part of the interest resides…
In a recent paper, 't Hooft asks for an integer version of Yang-Mills theory, in the belief that this is the way the universe really is at the Planck scale. Specifically, he asks for an integer version of the gauge group of the standard…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
The Einstein-Yang-Mills equations are the source of many interesting solutions within general relativity, including families of particle-like and black hole solutions, and critical phenomena of more than one type. These solutions,…
We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…