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The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…
We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
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 $h_0$.…
This article concerns the fate of local Lorentz invariance in quantum gravity, particularly for approaches in which a discrete structure replaces continuum spacetime. Some features of standard quantum mechanics, presented in a…
Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…
The classification of relevant, marginal and irrelevant operators is studied in the Randall-Sundrum spacetime. We find that there exist marginal and interacting operators in the Randall-Sundrum spacetime unlike a higher-dimensional…
We consider Lorentz-violating operators induced at the loop level in softly-broken supersymmetric noncommutative QED. Dangerous operators forbidden in the supersymmetric limit are generated via finite corrections, with the scale of…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there are local degrees of freedom one faces the "problem of dynamics". We attack it using the "uniform discretization…
We give a method of describing thermodynamical transport phenomena, based on a quantum scattering theoretical approach. We consider a quantum system of particles connected to thermodynamical reservoirs by leads. The effects of the…
A general form factor formula for the scaling Z(N)-Ising model is constructed. Exact expressions for matrix elements are obtained for several local operators. In addition, the commutation rules for order, disorder parameters and para-Fermi…
While general relativity possesses local Lorentz invariance, both canonical quantum gravity and string theory suggest that Lorentz invariance may be broken at high energies. Broken Lorentz invariance has also been postulated as an…
Currently, there are intense experimental efforts to realize lattice gauge theories in quantum simulators. Except for specific models, however, practical quantum simulators can never be fine-tuned to perfect local gauge invariance. There is…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…