相关论文: Partition function for the eigenvalues of the Wils…
The derivation of the explicit formula for the vacuum expectation value of the Wilson loop functional for an arbitrary gauge group on an arbitrary orientable two-dimensional manifold is considered both in the continuum case and on the…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
In quantum theory the vacuum is defined as a state of minimum energy that is devoid of particles but still not completely empty. It is perhaps more surprising that its definition depends on the geometry of the system and on the trajectory…
Graphene is a zero-gap semiconductor, where the electrons propagating inside are described by the ultra-relativistic Dirac equation normally reserved for very high energy massless particles. In this work, we show that graphene under a…
The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in…
In this note I revisit the calculation of partition function of simple one dimensional systems solvable by Bethe Ansatz. Particularly I show that by the precise definition and treatment of the partition function the nontrivial normalization…
For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner…
Particle-antiparticle pairs are predicted by quantum field theory to appear as vacuum fluctuations. The model of the vacuum used here is postulated to have the following properties: To minimize the violation of conservation energy allowed…
In a companion paper, we have developed a phase-space electronic structure theory of molecules in magnetic fields, whereby the electronic energy levels arise from diagonalizing a phase-space Hamiltonian $\hat H_{PS}(\bf{X},\bf{\Pi})$ that…
Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the Universal Confining String Theory, we derive for it the corresponding loop equation, alternative to the familiar one. In…
We consider a two parameter family of $Z_2$ gauge theories on a lattice discretization $T(M)$ of a 3-manifold $M$ and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space…
The thermal Wightman functions for free, massless particles of spin 0, 1/2, 1, 3/2, and 2 are computed directly in coordinate space by solving the appropriate differential equation and imposing the Kubo-Martin-Schwinger condition. The…
We compute the partition functions of $\mathcal{N} = 1$ gauge theories on $S^2 \times \mathbb{R}^2_\varepsilon$ using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of $S^2$ and at the origin of…
The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local $\zeta$-function regularization approach. The correct Planckian leading order…
Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted…
We consider the bifurcation problem u'' + \lambda u = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue \lambda. A new derivation of a variational principle for the lowest…
We exhibit a class of effective field theories that have hierarchically small Wilson coefficients for operators that are not protected by symmetries but are not finely tuned. These theories possess bounded target spaces and vacua that break…
Performing functional integration of the free Lagrangian, we find the vacuum energy of a field. The functional integration is performed in a way which easily generalizes to systems at non-zero temperature. We use this technique to obtain…
Taking (2+1)-dimensional pure Einstein gravity for arbitrary genus $g$ as a model, we investigate the relation between the partition function formally defined on the entire phase space and the one written in terms of the reduced phase…
There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. The resolution, a Hamiltonian system on a unified symplectic…