Related papers: Covariant Schwinger terms
In this survey article for the Encyclopedia of Mathematical Physics, 2nd Edition, I give an introduction to quantum character varieties and quantum character stacks, with an emphasis on the unification between four different approaches to…
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence of a second order integral of motion does not guarantee the…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
The proposal of the possibility of change of signature in quantum cosmology has led to the study of this phenomenon in classical general relativity theory, where there has been some controversy about what is and is not possible. We here…
We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The…
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
The quantum electromagnetic (EM) field is formulated in the Weyl-Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle it is possible to interpret within WW all experiments involving the EM…
We provide a minimal, self-contained introduction to the covariant DFR flat quantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an…
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
The recent formulation of locally covariant quantum field theory may open the way towards a background independent perturbative formulation of Quantum Gravity.
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
Although many people have thought that the difference between the Copenhagen and many-worlds versions of quantum theory was merely metaphysical, quantum cosmology may allow us to make a physical test to distinguish between them empirically.…
If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and…