Related papers: Classical and Quantum Theory with a New Symmetry
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
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…
The formation of singularities in certain situations, such as the collapse of massive stars, is one of the unresolved issues in classical general relativity. Although no complete theory of quantum gravity exists it is often suggested that…
In a previous work and in terms of an exact quantum-mechanical framework, $\hbar$-independent causal and retarded expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge were derived in the presence of a…
Classical gravitation theory is formulated as gauge theory on natural bundles where gauge symmetries are general covariant transformations and a gravitational field is a Higgs field responsible for their spontaneous symmetry breaking.
We argue that, ideally, the ways to measure magnitudes in non-quantum theories of physics (spacetime, field theory), limit drastically their possible mathematical models. In particular, gauge invariance in the Yang-Mills framework, is a…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded…
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
The gauge symmetry is one of the most important concepts in modern physics, but there are two conflicting views on its meaning or interpretation. The standard view is that local gauge symmetry is the basis of the pursue of fundamental…
When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which…
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…
It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat,…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB.…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…