相关论文: Path Integral Quantization of Volume

The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…

By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…

The three-dimensional Hilbert transform takes scalar data on the boundary of a domain in R3 and produces the boundary value of the vector part of a quaternionic monogenic (hyperholomorphic) function of three real variables, for which the…

Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the…

In this work the wave functions associated to the quantum relativistic universe, which is described by the Wheeler-DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark…

We describe a model of random links based on random 4-valent maps, which can be sampled due to the work of Schaeffer. We will look at the relationship between the combinatorial information in the diagram and the hyperbolic volume.…

We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation.…

We prove that $\W_3$ is the gauge symmetry of the scale-invariant rigid particle, whose action is given by the integrated extrinsic curvature of its world line. This is achieved by showing that its equations of motion can be written in…

The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…

A closed (in terms of classical data) expression for a transition amplitude between two generalized coherent states associated with a semisimple Lee algebra underlying the system is derived for large values of the representation highest…

The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time…

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area…

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection…

We compute explicitly the Riemannian volume, with respect to the Fubini-Study metric, of a domain bounded by a Hermitian quadric in complex projective space. The volume is a rational function of the eigenvalues of the defining quadratic…

In this paper the hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space of the theory has nontrivial…

Gibbons and Hawking proposed that the Euclidean gravity path integral with periodic boundary conditions in time computes the thermal partition sum of gravity. As a corollary, they argued that a derivative of the associated free energy with…

In the Feynman-Kac[1] path integral approach the eigenvalues of a quantum system can be computed using Wiener measure which uses Brownian particle motion. In our previous work[2-3] on such systems we have observed that the Wiener process…

We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The…

In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we…