PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

格点Z3规范场–Higgs场耦合体系的相结构

用Migdal–Kadanoff重整化群方法研究了四维时空中的格点Z₃规范场与Z₃-Higgs标量场耦合体系,得到了该体系的耦合常数递推关系和相图,结果表明Z3耦合体系的耦合常数递推关系中的项与Z₂、Z₄耦合体系的耦合常数递推关系中的项不存在一一对应关系.     

Exact Solutions of an Alice-Bob KP Equation *

An Alice-Bob Kadomtsev-Petviashivili (ABKP) equation with shifted-parity ($\hat{P}_s^x$ parity with a shift for the space variable $x$) and delayed time reversal ($\hat{T}_d$, time reversal with a delay) symmetries is investigated. The multi-soliton solutions with three arbitrary even or odd functions are found from the $\hat{P}_s^x\hat{T}_d$ symmetry reductions of a coupled local KP system. The result shows that for the ABKP equation with $\hat{P}_s^x\hat{T}_d$ nonlocality, the odd numbers of solitons are prohibited. The solitons of the ABKP must be paired. For the ABKPII equation, there exists a critical value of wave numbers for the existence of paired solitons. For the ABKPI equation, there are two types of "breather" excitations. A lump solution of the ABKPI may possess four, five or six leaves.     

Regge behaviour at high energy and more on boson-fermion interaction

Our approach to the problem of boson-fermion interaction in the conventional RFT stems from a model of super-symmetric version in 2-space and 1 time world. Basically it is stressed here that at super high energy there may not be any distinction between the bosonic and fermionic modes and may be treated on a common footing. Usual renormalization group approach for the vertex function has been adopted and the characteristic functionsβ ₁ andβ ₂ are calculated and the possibility of having stable points in the theory has been studied.     

Representation of Spin Group Spin（p, q）

The representation η（P, q） of spin group Spin（p, q） in any dimensional space is given by induction, and the relation between two representations, which are obtained in two kinds of inductions from Spin（p, q） to Spin（p ＋ 1, q ＋ 1） are studied.     

Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation

A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich–Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions.     

Spin Physics and the Theory of Strong Interactions

Taking the Minkowski space as the scene of quantum field theory implies an implicit assumption: the spin plays no dynamical role. This assumption (already challenged by reggeism) should be re-examined in the light of recent advances of experimental spin physics. To make a dynamical role of spin possible, it is proposed to use as a scene for the theory of strong interactions the whole Poincaré group. On the other hand characteristic functions, defined on the Poincare group, provide the only known way to describe the distinctive peculiarity of resonances, namely that a resonance is both one particle and several particles. Regge trajectories are interpreted as evidence for a mass-spin correlation among the virtual hadrons of vacuum. It is conjectured that the form of this correlation is deducible from a central limit theorem on the Poincare group. And that a statistical mechanics of hadronic vacuum is important for strong interaction theory.     

量子场论中的自旋算符

从量子场论的角度对相对论粒子的运动自旋概念作了进一步深入研究.构造了场量子自旋以及场系统运动自旋两个新算符.给出了场量子自旋动量空间的显式表达式以及用Poincar啨群生成元表示的场系统运动自旋的显式表达式.借助这两个算符,可以干净地解决有关场自旋的问题,表明它们才是场自旋的恰当的算符.     

Spin 1 Fields in Riemann-Cartan Space-Times via Duffin-Kemmer-Petiau Theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.     

Multi-place physics and multi-place nonlocal systems

Multi-place nonlocal systems have attracted attention from many scientists. In this paper, we mainly review the recent progresses on two-place nonlocal systems (Alice-Bob systems) and four-place nonlocal models. Multi-place systems can firstly be derived from many physical problems by using a multiple scaling method with a discrete symmetry group including parity, time reversal, charge conjugates, rotations, field reversal and exchange transformations. Multi-place nonlocal systems can also be derived from the symmetry reductions of coupled nonlinear systems via discrete symmetry reductions. On the other hand, to solve multi-place nonlocal systems, one can use the symmetry-antisymmetry separation approach related to a suitable discrete symmetry group, such that the separated systems are coupled local ones. By using the separation method, all the known powerful methods used in local systems can be applied to nonlocal cases. In this review article, we take two-place and four-place nonlocal nonlinear Schrödinger (NLS) systems and Kadomtsev-Petviashvili (KP) equations as simple examples to explain how to derive and solve them. Some types of novel physical and mathematical points related to the nonlocal systems are especially emphasized.     

Interacting Spin 0 Fields with Torsion via Duffin-Kemmer-Petiau Theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.On leave from     

Coset Structure of Spin Group

This article considers the coset structure of spin group via analyzing the expression of its representation.One example is also given to take a closer look at what the coset and the subgroup are.     

Tests of time-reversal invariance in complex systems

The random-matrix theory for the effects of time-reversal non-invariance (TRNI) on energy level, strength and cross-section fluctuations in complex systems is reviewed. Applied to the compound-nuclear data this gives bounds on rms TRNI matrix elements. Using a fluctuation-free form of statistical spectroscopy bounds on α, the relative magnitude of the TRNI nucleon-nucleon interaction, is deduced. In all three cases we find α ≲ (2–3) × 10⁻³ at high (∼ 99%) statistical confidence. Suggestions are made about experiments which should improve the bounds.     

并五苯分子电荷注入导致自旋极化的密度泛函理论研究

用密度泛函理论研究了不带自旋的空穴注入并五苯后体系的自旋相关特性. 电荷注入后并五苯分子中存在自发自旋极化行为. 当注入电荷量达一定程度,分子磁矩随注入电荷量的增加呈线性增长,最大磁矩可达1 μB. 注入电荷和并五苯分子的相互作用导致分子体系结构发生变化,同时电荷密度分布及自旋密度分布也发生了变化. 注入电荷先填充自旋劈裂的碳原子p_z轨道.     

Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

Effective-Field Theory on High Spin Systems with Biaxial Crystal Field

Based on the effective-field theory with self-spin correlations and the differential operator technique,physical properties of the spin-2 system with biaxial crystal field on the simple cubic, body-centered cubic, as well as faced-centered lattice have been studied. The influences of the external longitudinal magnetic field on the magnetization,internal energy, specific heat, and susceptibility have been discussed in detail. The phenomenon that the magnetization in the ground state shows quantum effects produced by the biaxial transverse crystal field has been found.