Quantum Prisoners’ Dilemma in Fluctuating Massless Scalar Field

Quantum systems are easily affected by external environment. In this paper, we investigate the influences of external massless scalar field to quantum Prisoners’ Dilemma (QPD) game. We firstly derive the master equation that describes the system evolution with initial maximally entangled state. Then, we discuss the effects of a fluctuating massless scalar field on the game’s properties such as payoff, Nash equilibrium, and symmetry. We find that for different game strategies, vacuum fluctuation has different effects on payoff. Nash equilibrium is broken but the symmetry of the game is not violated.     

Weyl invariance and the origins of mass

By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner–Freedman stability bounds in anti de Sitter amount to reality of these weights. The method relies on tractor calculus – mathematical machinery allowing Weyl invariance to be kept manifest at all stages. The equivalence between tractor and higher spin systems with arbitrary spins and masses is also considered.     

Internal space-time symmetries of particles derivable from periodic systems in optics

While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into three conjugate classes depending on their traces, optical systems force us to establish continuity from one class to another. It is noted that those three classes are equivalent to three different branches of Wigner’s little groups dictating the internal space-time symmetries massive, massless, and imaginary-mass particles. It is shown that the periodic systems in optics can also be described by the same class-based matrix algebra. The optical system allow us to make continuous, but not analytic, transitions from massiv to massless, and massless to imaginary-mass cases.     

Systems of covariance and subrepresentations of induced representations

In relativistic quantum physics, systems of covariance are used to describe the localizability of massless elementary systems. The notion of a system of covariance generalizes that of a system of imprimitivities by replacing the projection valued measure by a positive operator valued measure. Our main result concerns the constructibility of systems of covariance from systems of imprimitivities on different premises. As a corollary we get an analogous theorem to Mackey's Imprimitivity Theorem characterizing subrepresentations of induced representations.     

Dynamically generated anomalous magnetic moment in massless QED

In this paper we investigate the non-perturbative generation of an anomalous magnetic moment for massless fermions in the presence of an external magnetic field. In the context of massless QED in a magnetic field, we prove that the phenomenon of magnetic catalysis of chiral symmetry breaking, which has been associated in the literature with dynamical mass generation, is also responsible for the generation of a dynamical anomalous magnetic moment. As a consequence, the degenerate energy of electrons in Landau levels higher than zero exhibits Zeeman splitting. We explicitly report the splitting for the first Landau level and find the non-perturbative Lande g-factor and Bohr magneton. We anticipate that a dynamically generated anomalous magnetic moment will be a universal feature of theories with magnetic catalysis. Our findings can be important for condensed planar systems as graphene, as well as for highly magnetized dense systems as those forming the core of compact stars.     

Level spacing statistics for two-dimensional massless Dirac billiards

Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation(or Weyl equation)and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different,rendering distinct level spacing statistics.     

A classification of massless totally antisymmetric tensor field in arbitrary dimensional space-time

A formulation of the massless fields is given in terms of a system of first-order equations. There are two such systems, and the massless fields are accordingly classified into two families. Successive gauge transformations exist, by which the sequential FP ghosts are induced. The number of physical modes is counted easily by looking at the field strength.     

Non-commutative Geometry in Massless and Massive Particles

In this paper, we study the symmetries of massless and massive particles action. By considering the non-commutative space-time, we find appropriate non-commutative relation for relativistic particles which leaves invariant the non-commutative Minkowski space-time. We show that non-commutativity break the scale and conformal invariance in massless and massive action. So, in non-commutative space-time the massless and massive particles have same symmetry.     

Massless versus massive Hawking radiation in AdS2 spacetime

We study massless and massive Hawking radiations on a two-dimensional AdS spacetime. For the massless case, the quantum stress-energy tensor of a massless scalar field on the AdS background is calculated, and the expected null radiation is obtained. However, for the massive case, the scattering analysis is performed in order to calculate the absorption and reflection coefficients which are related to statistical Hawking temperature. On the contrary to the massless case, we obtain a nonvanishing massive radiation.     

Inclusive D^* production in photon-photon collisions at next-to-leading order QCD}

The next-to-leading order cross section for the inclusive production of charm quarks in collisions is calculated as a function of the transverse momentum and the rapidity y in approaches using massive or massless charm quarks. For the direct cross section we derive the massless limit from the massive theory with the result that this limit differs from the massless version with factorization by finite corrections. Subtracting or adding these corrections allows us to compare the two approaches on equal footing. We establish massless and massive versions with 3 and 4 initial flavours which are shown to approach the massless approximations very fast with increasing . With these results we calculate the inclusive cross section in collisions using realistic evolved fragmentation functions with appropriate factorization scales and compare with recent data for from three LEP collaborations after single- and double-resolved contributions have been added. Received: 25 September 2001 / Published online: 5 November 2001     

Gravitational scattering of massless scalars in QFT and superstring theory

In this paper we perform the calculation of the gravitational scattering amplitude for 4 massless scalars in quantum field theory and Type II superstring theory. We show that the results agree, providing an example of how gravity is incorporated in the superstring theory. During the calculation we quantize gravitational action to derive graviton propagator and interaction vertex with massless scalar. We also calculate general 3‐point and 4‐point scattering amplitudes in SST for open and closed massless strings in NS sector.     

Inclusive D production in $\gamma \gamma$ collisions: including the single-resolved contribution with massive quarks

We have calculated the next-to-leading order cross section for the inclusive production of charm quarks as a function of the transverse momentum p_T and the rapidity in two approaches using massive or massless charm quarks. For the single-resolved cross section we have derived the massless limit from the massive theory. We find that this limit differs from the genuine massless version with factorization by finite corrections. By adjusting subtraction terms we establish a massive theory with subtraction which approaches the massless theory very fast with increasing transverse momentum. With these results and including the equivalent results for the direct cross section obtained previously as well as double-resolved contributions, we calculate the inclusive cross section in collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the LEP collaborations ALEPH, L3 and OPAL. We find good agreement. Received: 14 February 2003 / Published online: 5 May 2003     

CPT/Lorentz invariance violation and neutrino oscillation

We analyze the consequences of violation of Lorentz and CPT invariance in the massless neutrino sector by deforming the canonical anti-commutation relations for the fields. We show that, for particular choices of the deformation, oscillation between massless neutrino species takes place when only Lorentz invariance is violated. On the other hand, if both Lorentz and CPT invariances are violated, we show that there is no oscillation between massless neutrino species. Comparing with the existing experimental data on neutrino oscillations, we obtain bounds on the parameter for Lorentz invariance violation.     

Excited TBA equations II: massless flow from tricritical to critical Ising model

We consider the massless tricritical Ising model perturbed by the thermal operator _1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massless thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A₄ lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandermonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.     

Cavity quantum chromodynamics to order αs2

Based on perturbative QCD in a cavity, we have calculated, for the two-quark and quark-antiquark systems, all non-diverging graphs to order α_s² which do not involve additional quark-antiquark pairs in the intermediate states. Using the two-body interactions that include the two-gluon exchange and annihilation graphs, we obtain a fit to the low-energy spectrum of hadrons consisting of massless quarks and anti-quarks, in particular the splitting of the masses of the π- and η-mesons.     

Single Transverse Spin Asymmetries at Parton Level

Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other is the transverse-momentum-dependent factorization. They have been previously derived in a formal way by using diagram expansion at hadron level. If the two factorizations hold or can be proven, they should also hold when we replace hadrons with patton states. We examine these two factorizations at patton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless patrons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable patton states with massless partons we derive the two factorizations for the asymmetry in Drell-Yan processes. It is found from our results that the collinear factorization derived at parton level is not the same as that derived at hadron level. Our results with massless partons confirm those derived with single massive parton state in our previous works.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.