Related papers: Time operator in QFT with Virasoro constraints
It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed.
We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics some properties of solutions of Schroedinger equation, related to Hilbert space formalism, are investigated for two types of time dependent…
We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…
For testing hypothesis on the covariance operator of functional time series, we suggest to use the full functional information and to avoid dimension reduction techniques. The limit distribution follows from the central limit theorem of the…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
We study the Fock description of a quantum free field on the three-sphere with a mass that depends explicitly on time, also interpretable as an explicitly time dependent quadratic potential. We show that, under quite mild restrictions on…
In single Hilbert space, Pauli's well-known theorem implies that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian signifies that the time operator and the Hamiltonian possess completely continuous…
In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
There is no self adjoint time operator defined in quantum mechanics. However, time intervals can be defined in several ways and can also be probed experimentally. Our interest in this work is traversal time and signal propagation time.…
Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of…
A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…
The aim of this work is to further study the fractional bosonic string theory. In particular, we wrote the energy-momentum tensor in the fractional conformal gauge and study their symmetries. We introduced the Virasoro operators of all…
Contrary to the conviction expressed by J. Kijowski [Phys. Rev. A 59, 897 (1999)] and shared in some other papers, the reasons to look for the 'time operator' in the context of the standard quantum doctrine of orthogonal projectors and…
Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) is shown to provide a unified origin for: i) the complex vector space formulation of Quantum Mechanics (QM); ii) the momentum…