Related papers: General ordering theorem
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable…
We construct an effective field theory (EFT) that captures the universal behavior of out-of-time-order correlators (OTOCs) at late times in generic quantum many-body systems with conservation laws. The EFT hinges on a generalization of the…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light $c$ not being infinite calls for a redefinition of space-time on large and cosmological scales,…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body…
In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Newmann for symmetric operators in order to determine whether the…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…
Interactions are explored through the observation of the dynamics of particles. On the classical level the basic underlying assumption in that scheme is that Newton's second law holds. Relaxing the validity of this axiom by, e.g., allowing…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport moments reduce to codifying classical correlations between…