相关论文: On Polyakov's basic variational formula for loop s…
We investigate the effective action of the Polyakov loop with spatial variations. We expand the effective action not in powers of derivatives or momenta, but in powers of variational amplitudes. At one-loop order the results suggest that…
In this paper we calculate the integral Pontrjagin homology ring of the based loop space on some generalised symmetric spaces with a toral stationary subgroup. In the Appendix we show that the method can be applied to other type generalised…
We prove that generalized loop spaces of Hartogs manifolds are Hilbert-Hartogs. We prove also that Hilbert-Hartogs manifolds possess a better extension properties that it is postulated in their definition. Finally, we give a list of…
We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie…
We study the spatial inhomogeneity of the Polyakov loop induced by inhomogeneous chiral condensates. We formulate an effective model of gluons on the background fields of chiral condensates, and perform its lattice simulation. On the…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
In this paper we will first construct Polyakov loops for the ABJ theory. Then we will construct the connection and curvature in this loop space. We will also analyse certain generalization of Polyakov loops and apply them to the ABJ theory.…
In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces…
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function spaces on hypergraphs. Several results related to the…
The lower order terms of the heat kernel expansion at coincident points are computed in the context of finite temperature quantum field theory for flat space-time and in the presence of general gauge and scalar fields which may be non…
For a spectrum $X$ represented by a special $\Gamma$-space $Y$ via the Segal machine, we give an elementary formula computing the homology groups of $X$ in terms of $Y$. Both the result and the method of proof are essentially due to T.…
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology…
A technical point regarding the invariance of Polyakov's nonlocal form of the effective action under uniform rescalings is briefly addressed.
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.
We study rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements…
The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of functionals on fields should be read as a…
Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a…
We give an extension of the theory of relaxation of variational integrals in classical Sobolev spaces to the setting of metric Sobolev spaces. More precisely, we establish a general framework to deal with the problem of finding an integral…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.