相关论文: Central extensions and quantum physics

Holomorphy of the superpotential promotes any continuous symmetry group G to a complexified symmetry group G_C of the superpotential. For U(1) symmetry this means that the superpotential is not only invariant under U(1) phase rotation but…

An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and…

It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…

The formulation and some experimental implications of a general Lorentz-violating extension of the standard model are reviewed. The theory incorporates both CPT-preserving and CPT-breaking terms. It is otherwise a conventional quantum field…

We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…

Generic relevant deformations of Einstein's gravity theory contain additional degrees of freedom that have a multi-facetted stabilization dynamics on curved spacetimes. We show that these relevant degrees of freedom are self-protected…

A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…

Quantum gravitational corrections to the effective potential, at one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity ---which is taken as an effective theory for quantum…

A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…

We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…

A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…

We derive the scalar-tensor Hamiltonian constraint to all orders of momenta when the canonical constraint algebra is deformed by a phase space function as predicted by some studies into loop quantum cosmology. We find that the momenta and…

It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…

Gauge symmetries generally appear as a constraint algebra, under which one expects all physical states to be singlets. However, quantum anomalies and boundary conditions introduce central charges and change this picture, thus causing…

A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and a condition is additionally imposed on the latter that ensures the classical character…

We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…

Improving on an earlier proposal, we construct the gauge theories of the quantum groups $U_q(N)$. We find that these theories are consistent also with an ordinary (commuting) spacetime. The bicovariance conditions of the quantum…

The physics of individual Q-balls and interactions between multiple Q-balls are well-studied in classical numerical simulations. Interesting properties and phenomena have been discovered, involving stability, forces, collisions and swapping…

General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…