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The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium…
In classical physics the energy density of a field, such as the electromagnetic field, is always positive. However, in quantum field theory it has been shown that the energy density can be negative. There are restrictions, called the…
In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical…
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
We show that Hall conductance and its non-abelian and higher-dimensional analogs are obstructions to promoting a symmetry of a state to a gauge symmetry. To do this, we define a local Lie algebra over a Grothendieck site as a pre-cosheaf of…
After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in…
This is mainly a lecture note taken by myself following Weinberg's book, but also contains some corrections to the abuse of mathematical treatment. This article discusses projective unitary representations of Poincare group on the single…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
We encapsulate the basic notions of the theory of vertex algebras into the construction of a comonad on an appropriate category of formal distributions. Vertex algebras are recovered as coalgebras over this comonad.
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
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…
In this letter we address some of the issues raised in the literature about the conflict between a large vacuum energy density, apriori predicted by quantum field theory, and the observed dark energy which must be the energy of vacuum or…
Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.