相关论文: A conserved Parity Operator
The concept of parity describes the inversion symmetry of a system and is of fundamental relevance in the standard model, quantum information processing, and field theory. In quantum electrodynamics, parity is conserved and large field…
The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable…
We explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse…
The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss…
Parity-time-reversal symmetry ($\mathcal{PT}$ symmetry), a symmetry for the combined operations of space inversion ($\mathcal{P}$) and time reversal ($\mathcal{T}$), is a fundamental concept of physics and characterizes the functionality of…
Various versions of the definition of nonclassical symmetries existing in the literature are analyzed. Comparing properties of Lie and nonclassical symmetries leads to the conclusion that in fact a nonclassical symmetry is not a symmetry in…
It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
The characterization mentioned in the title is found.
This article rebuilds the parity conservation under the light of Heinsenberg's uncertainty principle and the equivalence among the four space-time coordinates. The lack of equilibrium between matter and antimatter is elucidated; neutrino…
The Composite Operator Method (COM) is formulated, its internals illustrated in detail and some of its most successful applications reported. COM endorses the emergence, in strongly correlated systems (SCS), of composite operators,…
We consider some multivariate rational functions which have (or are conjectured to have) only positive coefficients in their series expansion. We consider an operator that preserves positivity of series coefficients, and apply the inverse…
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators…
This two-part article considers certain fundamental symmetries of nature, namely the discrete symmetries of parity (P), charge conjugation (C) and time reversal (T), and their possible violation. Recent experimental results are discussed in…
Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group. These representations are connected with Wilson polynomials.
It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and…
In understanding the world of matter, the introduction of symmetry principles following experimentation or using the predictive power of symmetry principles to guide experimentation is most profound. The conservation of energy, linear…
We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that…