A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

Common vacuum conservation amplitude in the theory of the radiation of mirrors in two-dimensional space-time and of charges in four-dimensional space-time

The changes in the action (and thus the vacuum conservation amplitudes) in the proper-time representation are found for an accelerated mirror interacting with scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to within a factor of e ² with changes in the action of electric and scalar charges accelerated in 3+1 space. This coincidence is attributed to the fact that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0 as do the photons and scalar quanta emitted by charges. It is shown that the propagation of virtual pairs in 1+1 space can be described by the causal Green’s function Δ_f(z,μ) of the wave equation for 3+1 space. This is because the pairs can have any positive mass and their propagation function is represented by an integral of the causal propagation function of a massive particle in 1+1 space over mass which coincides with Δ_f(z,μ). In this integral the lower limit μ is chosen small, but nonzero, to eliminate the infrared divergence. It is shown that the real and imaginary parts of the change in the action are related by dispersion relations, in which a mass parameter serves as the dispersion variable. They are a consequence of the same relations for Δ_f(z, μ). Therefore, the emergence of a real part in the change in the action is a direct consequence of causality, according to which Re Δ_f(z,μ)≠0 only for timelike and lightlike intervals. Zh. éksp. Teor. Fiz. 116, 1523–1538 (November 1999)     

All spin-2 cubic vertices with two derivatives

In this paper we provide a complete list of spin-2 cubic interaction vertices with two derivatives. We work in (anti) de Sitter space with dimension d?4$d?4$ and arbitrary value of cosmological constante and use simple metric formalism without any auxiliary or Stueckelberg fields. We separately consider cases with one, two and three different spin-2 fields entering the vertex where each field may be massive, massless or partially massless one. The connection of our results with massive (bi)gravity theories is also briefly discussed.     

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(N_c) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an N_f window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is N_f^cr=10.0±0.29 (fermion)^+1.55_-0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively. PACS 11.10.Hi, 11.15.Tk, 11.30.Rd     

Spin-3 topologically massive gravity

In this Letter, we study the spin-3 topologically massive gravity (TMG), paying special attention to its properties at the chiral point. We propose an action describing the higher spin fields coupled to TMG. We discuss the traceless spin-3 fluctuations around the AdS₃ vacuum and find that there is an extra local massive mode, besides the left-moving and right-moving boundary massless modes. At the chiral point, such extra mode becomes massless and degenerates with the left-moving mode. We show that at the chiral point the only degrees of freedom in the theory are the boundary right-moving graviton and spin-3 field. We conjecture that spin-3 chiral gravity with generalized Brown-Henneaux boundary condition is holographically dual to 2D chiral CFT with classical W₃ algebra and central charge cR=3l/G.     

Moduli and (un)attractor black hole thermodynamics

We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS ₂ × S ² and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen’s entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza–Klein black hole.     

On Vacuum Fluctuations and Particle Masses

The idea that the mass m of an elementary particle is explained in the semi-classical approximation by quantum-mechanical zero-point vacuum fluctuations has been applied previously to spin-1/2 fermions to yield a real and positive constant value for m, expressed through the spinorial connection Γ _i in the curved-space Dirac equation for the wave function ψ due to Fock. This conjecture is extended here to bosonic particles of spin 0 and spin 1, starting from the basic assumption that all fundamental fields must be conformally invariant. As a result, in curved space-time there is an effective scalar mass-squared term , where R is the Ricci scalar and Λ _b is the cosmological constant, corresponding to the bosonic zero-point energy-density, which is positive, implying a real and positive constant value for m ₀, through the positive-energy theorem. The Maxwell Lagrangian density for the Abelian vector field F _ij ≡A _j,i −A _i,j is conformally invariant without modification, however, and the equation of motion for the four-vector potential A _i contains no mass-like term in curved space. Therefore, according to our hypothesis, the free photon field A _i must be massless, in agreement with both terrestrial experiment and the notion of gauge invariance.     

Conformal symmetry breaking and mass generation

We consider an extension of the supersymmetry formalism in order to include gauge fields. We construct a fiber bundle P(M ₄×{θ}, G) over the superspace with the gauge group as the structural group. We obtain the equations of interacting pure Yang-Mills and massless Higgs fields, considering these fields as the components of the same gauge field. Moreover, by fixing a gauge we generate a mass as a result of the supersymmetry breaking. Supported by Instituto Nacional de Investigacao Cientifica (Lisboa).     

Quark-lepton compositeness: A three-body scenario

The Harari-Shupe model of quarks and leptons is viewed, not as a gauge theory, but as a quantum-mechanical three-body problem of the extreme relativistic type involving massless preons. Considerations based onS ₃-symmetry in the available degrees of freedom (spin, isospin, space and hypercolour) are employed in conjunction with a spin-dependence ansatz on the three-preon forces (Σ ^a =σ _μv ⁽¹⁾ σ _λμ ⁽³⁾ ) for an understanding of the three basic issues of (i) spin-1/2, (ii) generation structure and (iii) steeply rising mass patterns of quark-lepton families. The Σ ^a -dynamics is compatible with the interpretation of colour as a manifestation ofS ₃-symmetry, as envisaged in the original Harari-Shupe proposal, while the interpretation of the generation structure devolves on the role of a certain quantum numberN which takes on three different classes of values (3n, 3n ± 1;n = 0, 1, 2, ...) according to theS ₃-symmetry of thespatial wavefunction.     

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. Received: 8 September 2001 / Accepted: 18 March 2002     

Regularization as Quantization in Reducible Representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials (an alternative to the Gupta-Bleuler method) is tested on the example of quantum electromagnetic fields produced by a classical current. The Heisenberg dynamics can be consistently formulated since the fields are given by operators and not operator-valued distributions. The scheme involves a Hamiltonian whose free part is modified but the minimal-coupling interaction is the standard one. Solving Heisenberg equations of motion under the assumption that the fields are free for times t ₀ = ±∞ we arrive at retarded and advanced solutions. Once we have these solutions we can deduce the form of evolution of retarded and advanced fields between two arbitrary finite times. The appropriate unitary evolution operators are found and their generators are computed. Now the generators involve the same free part as before, but the interaction term turns out to be modified. For a pointlike charge localized on a world-line z ^a (t) we find the interaction term of the form where the integration is along those parts of the charge world-line where the charge velocity is nonzero. There is no self-energy contribution. Next we compute photon statistics. Poisson statistics naturally results and infrared divergence can be avoided even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincaré covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to Rényi’s α. It is shown that the “Shannon limit” α→ 1 plays here a role of a correspondence principle with the standard regularized formalism. PACS: 03.70.+k, 41.20.Jb, 42.50.-p.     

Slow Motion of Charges¶Interacting Through the Maxwell Field

We study the Abraham model for N charges interacting with the Maxwell field. On the scale of the charge diameter, R _ϕ, the charges are a distance ɛ^-1 R _ϕ apart and have a velocity with ɛ a small dimensionless parameter. We follow the motion of the charges over times of the order ɛ^-3/2 R _ϕ/c and prove that on this time scale their motion is well approximated by the Darwin Lagrangian. The mass is renormalized. The interaction is dominated by the instantaneous Coulomb forces, which are of the order ɛ². The magnetic fields and first order retardation generate the Darwin correction of the order ɛ³. Radiation damping would be of the order ɛ^7/2. Received: 13 January 2000 / Accepted: 4 February 2000     

Speed of light in non-trivial vacua

We unify all existing results on the change of the speed of low-energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than c depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low-energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass related, or running mass-related. We also develop a formalism for the Casimir vacuum which parallels the thermal one and check that photons travel faster than c between plates.     

Temperature-dependent particle production and stimulated emissions by external sources

Exact solutions for transition amplitudes for particle production and stimulated emission by external sources are derived forfinite temperatures. More precisely, we obtain the expressions for amplitudes for the emission of an arbitrary number of particles by the sources, and correspondingstimulated emission processes, when one is dealing with a generalized multiparticle state (rather than the vacuum) at finite temperatures. The solutions are given for spin-0, massive and massless (photons) spin-1, and spin-1/2 particles. As applications, we study the process: photon any photons, in the presence of a strong external electromagnetic current, with the net release of a specified energy, and work out the power radiated by a given electromagnetic current distribution, all at finite temperatures. The latter application includes the radiation emitted by a point charged particle atT 0 as a special case.     

Exact solutions for stimulated emissions by external sources

The exact solutions for transition amplitudes are derived forstimulated emissions by external sources. More precisely, we obtain the exact expressions for transition amplitudes for the emission of an arbitrary number of particles by the sources when some particles are already present, in the process,prior to the switching on of the external sources. The solutions are given for an arbitrary number of particles with arbitrary configurations (of momenta, spin, etc.) and for particles of spin-0, spin-1/2, massive and massless (photons) spin-1 particles, and massless (gravitons) spin-2 particles. Applications are given as illustrations to the process Ø anything, and, in quantum electrodynamics, to the process e ⁺e^–+ any photons, in thepresence of external sources, where a (virtual) photon decays into the paire ⁺e^–.