Related papers: Origin of the anomalies: the modified Heisenberg e…
Quantization of field-theoretic models with gauge symmetries is often obstructed by quantum anomalies. It is commonly believed that the origin of these anomalies lies in the infinite number of degrees of freedom, which requires completing…
In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting…
The Hamiltonian defines the dynamical properties of the universe. Evidence from particle physics shows that there is a different version of the Hamiltonian for each direction of time. As there is no physical basis for the universe to be…
We show via an explicit example that quantum anomalies can lead to decoherence of a single quantum qubit through phase relaxation. The anomaly causes the Hamiltonian to develop a non-self-adjoint piece due to the non-invariance of the…
The holographic principle is represented as the well-known de Alfaro, Fubini and Furlan correspondence between the generating functional for the Green functions of the Euclidean quantum field theory in $D$ dimensions and the Gibbs average…
This papers deals with connections between quantum anomalies and transformations of Feynman pseudo-measures. Mathematical objects related to the notion of the volume element in an infinite-dimensional space considered in the physics…
We present two lines of investigation involving anomalies. First, we review mechanisms behind the classical and quantum conservation of symmetries using functional integration. This discussion clarifies conditions for quantum violations, as…
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to…
The well known and oft-quoted Feynman's expression, entered the title, leading at a loss and even being objectionable, has not yet a clear explanation. The hidden parameters problem in quantum mechanics is considered here on the base of…
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…
Quantum Mechanics of the Early Universe is considered as deformation of a well-known Quantum Mechanics. Similar to previous works of the author, the principal approach is based on deformation of the density matrix with concurrent…
An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in…
Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
We show that a differential variant of the Heisenberg uncertainty relations emerges naturally from induced matter theory, as a sum of line elements in both momentum and Minkowski spaces.
Puzzles associated with Yukawa's mesotron theory of nuclear interactions led to the discovery of "anomalies" in quantum field theory. I will discuss some of the remarkable consequences of these anomalies in the physics of elementary…
Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the…