We obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium distribution.We show that for the Juttner equilibrium distribution the relativistic diffusion is a linear approximation to the Kompaneetz equation describing a photon diffusion in an electron gas.The stochastic equation corresponding to the Juttner distribution is explicitly soluble. We relate the relativistic diffusion to imaginary time quantum mechanics. Some astrophysical applications (including the Sunyaev-Zeldovich effect) are briefly discussed.
This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic co…
We consider the action of the $q$-deformed Poincaré superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable $AdS_2 \times S^2 \times T^6$ type IIB superstring theory. The boost generator acts non-trivially on the R-matrix, confirming the existence of a non-relativistic rapidity $γ$ with respect to which the R-matrix must be of difference form. We conjecture that from a massless AdS/CFT integrable relativistic R-matrix one can obtain the parental massless non-relativistic R-matrix simply by replacing the relativistic rapidity with $γ$. We check our conjecture …
We give a simple and direct construction of a massless quantum field with arbitrary discrete helicity that satisfies Wightman axioms and the corresponding relativistic wave equation in the distributional sense. We underline the mathematical differences to massive models. The construction is based on the notion of massless free net (cf. Section 3) and the detailed analysis of covariant and massless canonical (Wigner) representations of the Poincare' group. A characteristic feature of massless models with nontrivial helicity is the fact that the fibre degrees of freedom of the covariant and cano…
We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H= sum{i=1 to N} sqrt(p_i^2)+ sum{j>i=1 to N} g |r_i - r_j|^2, g > 0. We prove the inequalities A [g N^2 (N-1)^2]^{1/3} < E < B [g N^2 (N-1)^2]^{1/3}, where A = 2.33810741 and B = [81/(2 pi)]^{1/3} = 2.3447779. The average of these bounds determines E with an error less than 0.15% for all N > 1.
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
In this work, the relativistic non-standard Lagrangian densities (k-fields) with massless solutions are generally introduced. Such solutions are not necessarily energetically stable. However, in 3+1 dimensions, we introduce a new k-field model that results in a single non-topological massless solitary wave solution. This special solution is energetically stable; that is, any arbitrary deformation above its background leads to an increase in the total energy. In other words, its energy is zero which is the least energy in all solutions. Hence, it can be called a massless soliton solution.
We propose a new world-line Lagrangian model of the D=4 massless relativistic particle with continuous spin and develop its twistorial formulation. The description uses two Penrose twistors subjected to four first class constraints. After the first quantization of the world-line twistorial model, the wave function is defined by an unconstrained function on the two-dimensional complex affine plane. We find the twistor transform that determines the space-time field of the continuous spin particle through the corresponding twistor one, which plays the role of a prepotential. It is shown that this…
We consider a Haag-Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that states of the massive particles are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis we use our new technique to further simplify scatterin…
We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry transformations are discussed for the first-order Lagrangian of the system where the transformations on the coordinates, velocities and momenta play very important roles. We discuss the dynamics of this system in a systematic manner by exploiting the symplectic structures associated with the four dimensional (non-)commutative cotangent (i.e. momentum phase) spac…
We study several formulations of zero-mass relativistic equations, stressing similarities between different frameworks. It is shown that all these massless wave equations have fermionic as well as bosonic solutions.
In the framework of light-cone formulation of relativistic dynamics, arbitrary spin massless fields propagating in the four-dimensional AdS space are studied. For such fields, the complete list of light-cone gauge cubic interaction vertices is obtained. Realization of relativistic symmetries on space of light-cone gauge massless AdS fields is also obtained. The light-cone gauge vertices for massless AdS fields take simple form similar to the one for massless fields in the flat space.
We show that the massless integrable sector of the AdS_3 \times S^3 \times T^4 superstring theory, which admits a non-trivial relativistic limit, provides a setting where it is possible to determine exact minimal solutions to the form factor axioms, in integral form, based on analiticity considerations, along the same lines of ordinary relativistic integrable models. We construct in full detail the formulas for the two- and three-particle case, and show the similarities as well as the differences with respect to the off-shell Bethe ansatz procedure of Babujian et al. We show that our expressio…
A Poincaré covariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin $s>1/2$ in four-dimensional Minkowski space. By making use of this Lagrange anchor, we assign a symmetry to each conservation law and perform the path-integral quantization of the theory.
We discuss a non-relativistic contraction of massive and massless field theories minimally coupled to gravity. Using the non-relativistic limiting procedure introduced in our previous work, we (re-)derive non-relativistic field theories of massive and massless spins 0 to 3/2 coupled to torsionless Newton-Cartan backgrounds. We elucidate the relativistic origin of the Newton-Cartan central charge gauge field $m_μ$ and explain its relation to particle number conservation.
We first analyse the integrable scattering theory describing the massless excitations of $AdS_2 \times S^2 \times T^6$ superstrings in the relativistic limit. The matrix part of the S-matrix is obtained in the BMN limit from the conjectured exact expression, and compared with known S-matrices with N=1 supersymmetry. A dressing factor, yet unknown for the complete theory, is here constructed based on relativistic crossing symmetry. We derive a Bethe-ansatz condition by employing a transfer-matrix technique based on the so-called free-fermion condition. This is known to overcome the problem of l…
We demonstrate how a classical Snyder-like phase space can be constructed in the Hamiltonian formalism for the free massless relativistic particle, for the two-time physics model and for the relativistic Newtonian gravitodynamic theory. In all these theories the Snyder-like phase space emerges as a consequence of a new local scale invariance of the Hamiltonian. The implications and consequences of this Snyder-like phase space in each of these theories are also considered.
Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the causal structure of Minkowski spacetime are illustrated by exploring the conflicts arising from localization and causal properties commonly imposed on single particle states. These topics necessitate the introduction of quantum field theoretical localization concepts and are scarcely discussed and often misinterpreted in the literature.
A natural presymplectic structure for non-Lagrangian equations of motion governing the dynamics of free higher-spin fields in four-dimensional anti-de Sitter space is proposed. This presymplectic structure is then used to the derivation of the conserved currents associated with the relativistic invariance and to the construction of local functionals of fields that are gauge invariant on shell.
In this work, we derive from first principles the relativistic wave equation of massless particles of arbitrary helicity. We start from unitary projective irreducible representations of the restricted Poincaré group. We define a weaker notion of localization and find, in particular, a position operator for any massless particle of arbitrary helicity. Therefore, having the position representation for these particles, we obtain the wave equations in this representation. We compare our results with previous findings in the literature.
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive relativistic particles with spin zero and spin-1/2 are expressed in terms of the principal series of the unitary representations of the Lorentz group. We also consider the massless case. New Hamilton operators are conctructed for the massless particles with spin zero and spin 1/2.
Closed-form expressions for smeared bi-distributions of a massless scalar field: non-perturbative and asymptotic results in relativistic quantum information
It is investigated if massless particles can couple to scalar fields in a special relativistic theory with classical particles. The only possible obvious theory which is invariant under Lorentz transformations and reparametrization of the affine parameter leads to trivial trajectories (straight lines) for the massless case, and also the investigation of the massless limit of the massive theory shows that there is no influence of the scalar field on the limiting trajectories. On the other hand, in contrast to this result, it is shown that massive particles are influenced by the scalar field in …
We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is described by a unitary irreducible representation of the Poincare group realized in the Hilbert space of wave functions in the momentum space. The arbitrariness of the Wigner rotation appears as a gauge freedom of the diffusion equation. The spin is described as a connection of a fiber bundle over the momentum hyperbolic space (the mass-shell). Motion in an…
We study a relativistic diffusion equation on the Riemannian phase space defined by Franchi and Le Jan. We discuss stochastic Ito (Langevin) differential equations (defining the diffusion) as a perturbation by noise of the geodesic equation. We show that the expectation value of the angular momentum and the energy grow exponentially fast. We discuss drifts leading to an equilibrium. It is shown that the diffusion process corresponding to the Juettner or quantum equilibrium distributions has a bounded expectation value of angular momentum and energy. The energy and the angular momentum tend exp…
A new two-dimensional black hole model, based on the "R=T" relativistic theory, is introduced, and the quantum massless scalar field is studied in its classical gravitational field. In particular infrared questions are discussed. The two-point function, energy-momentum tensor, current, Bogoliubov transformations and the mean number of created particles for a given test function are computed. I show that this black hole emits massless scalar particles spontaneously. Comparison with the corresponding field theory in a thermal bath shows that the spontaneous emission is everywhere thermal, i.e. n…
We explicitly calculate the $AdS_2 \times S^2 \times T^6$ transfer-matrix eigenvalues in the massless sector using the exact integrable S-matrix, for up to 5 particles. This enables us to conjecture the general pattern. We use the conjectured form of the eigenvalues to write down a set of massless Bethe ansatz equations. The same procedure applies to the relativistic as well as to the non-relativistic situation. In the relativistic case, the right and left modes decouple. We speculate that the relativistic massless Bethe ansatz we obtain in that case might capture the integrable structure of a…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides t…
The Penrose transform between twistors and the phase space of massless particles is generalized from the massless case to an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or non-relativistic, interacting or non-interacting, in flat space or curved spaces. Our unified construction involves always the \it{same} twistor Z^A with only four complex degrees of freedom and subject to the \it{same} helicity constraint. Only the twistor to phase space transform differs from one case to another. Hence a unification of diverse pa…
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature β^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).
We identify momentum/helicity probability amplitudes for the photon and find their relativistic transformation properties. We also find their behaviour under space inversion and time reversal. The discussion begins with a review of the unitary, irreducible representations of the Poincare group for massless particles. The little group, the set of Lorentz transformations that leave the momentum unchanged, is distinctly different for massless particles compared to the little group of rest frame rotations for a massive particle. We give a physical interpretation of the little group for a massless …
We discuss relativistic dynamics in a random electromagnetic field which can be considered as a high temperature limit of the quantum electromagnetic field in a heat bath (cavity) moving with a uniform velocity w. We derive diffusion approximation for the particle's dynamics generalizing the diffusion of Schay and Dudley. It is shown that the Juttner distribution is the equilibrium state of the diffusion.
We present a study of the thermodynamics of the massless free Dirac field at equilibrium with axial charge, angular momentum and and external electromagnetic field to assess the interplay between chirality, vorticity and electromagnetic field in relativistic fluids. After discussing the general features of global thermodynamic equilibrium in quantum relativistic statistical mechanics, we calculate the thermal expectation values. Axial imbalance and electromagnetic field are included non-perturbatively by using the exact solutions of the Dirac equation, while a perturbative expansion is carried…
The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz invariance violation. It is shown that this deformation does not affect the propagation speed of free massless particles. From the deformation of the dispersion relation for massless particles, gamma ray burst data is used to establish an upper bound on the noncommutative parameter, $η$, namely $\sqrtη \lesssim 10^{-12} \,\mathrm{eV/c}$. Additionally, a putative …
We analyze the signal-to-noise ratio for a relic background of scalar gravitational radiation composed of massive, non-relativistic particles, interacting with the monopole mode of two resonant spherical detectors. We find that the possible signal is enhanced with respect to the differential mode of the interferometric detectors. This enhancement is due to: {\rm (a)} the absence of the signal suppression, for non-relativistic scalars, with respect to a background of massless particles, and {\rm (b)} for flat enough spectra, a growth of the signal with the observation time faster than for a mas…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the proper time. We study the stochastic processes solving the relativistic diffusion equation and the relativistic transport equation. We show that the relativistic transport equation for massive particles in the light cone coordinates and for massless particles in spatial momentum coordinates are related to the (generalized) Bessel diffusion which has an analytic …
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore a…
We study the space-time invariances of the relativistic particle action for both the massive and massless cases. While the massive action has only the invariances associated to the Poincare algebra, we find that the invariances of the massless action give rise to the conformal algebra in four dimensions. For the free massless particle, a new invariance of the action permits the construction of an extension of the conformal algebra. The conclusion is that two distinct symmetry breaking mechanisms are necessary to arrive at the Poincare algebra.
We consider Wong equations for a particle with a continuous mass spectrum in a random Yang-Mills field approximating the quantum field at finite temperature. We show that particle time evolution can be approximated by a relativistic diffusion. Kubo's generator of the relativistic diffusion is defined as an expectation value of the square of the Liouville operator.
We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form.We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution.We discuss drag terms leading to …
We investigate in some detail the structure of the electromagnetic current density for the pseudo-relativistic massless spinor effective model for graphene. It is shown that the pseudo-relativistic massless Dirac field theory in {\em 2+1} space-time dimensions and in the presence of a constant homogeneous electric field actually leads to the measured current density and to the minimum quantum conductivity.
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant Coefficient Hypothesis contends that this familiar construction by itself yields useful results. Thus, just the transformation properties are considered here, not the specific properties of annihilation or creation operators. The results include Weyl wave equations for some massless fields and, for other fields, Weyl-like noncovariant wave equations that are allo…
In this paper, we discuss dissipation process of the binary mixture gas in the thermally relativistic flow \textcolor{red}{by focusing on the characteristics of the diffusion flux}. As an analytical object, we consider the relativistic rarefied-shock layer problem around the triangle prism. Numerical results of the diffusion flux are compared with the Navier-Stokes-Fourier (NSF) order approximation of the diffusion flux, which is calculated using the diffusion and thermal-diffusion coefficients by Kox \textit{et al}. [Physica A, 84, 1, pp.165-174 (1976)]. In the case of the uniform flow with t…
It is shown that dynamics of D+2 elements of the (super)diffeomorphism group in one (1+1 for the super) dimension describes the D - dimensional (spinning) massless relativistic particles. The coordinates of this elements (D+2 einbeins, D+2 connections and 1 additional common coordinate of higher dimensionality) play the role of coordinates, momenta and Lagrange multiplier, needed for the manifestly conformal and reparametrization invariant description of the D - dimensional (spinning) particle in terms of the D+2 - dimensional spacetime.
We investigate the vacuum pp-wave and Aichelburg-Sexl-type solutions in f(R) and the modified Gauss-Bonnet theories of gravity with both minimal and nonminimal couplings between matter and geometry. In each case, we obtain the necessary condition for the theory to admit the solution and examine it for several specific models. We show that the wave profiles are the same or proportional to the general relativistic one.
On the simple model of interacting massless and heavy scalar fields it is demonstrated that the technique of heavy baryon chiral perturbation theory reproduces the results of relativistic theory. Explicit calculations are performed for diagrams including two-loops.
The Bethe-Salpeter equation for two massive scalar particles interacting by scalar massless exchange has solutions of two types, which differ from each other by their behavior in the non-relativistic limit: the normal solutions which turn into the Coulomb ones and the "abnormal" solutions. The latter ones have no non-relativistic counterparts and disappear in the non-relativistic limit. We studied the composition of all these states. It turns out that the normal states, even for large binding energy, are dominated by two massive particles. Whereas, the contribution of the two-body sector into …
We present a path integral representation for massless spin one-half particles. It is shown that this gives us a super-symmetric, P-and T-non-invariant pseudoclassical model for relativistic massless spinning particles. Dirac quantization of this model is considered.
We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit any massless particle with a two dimensional internal degree of freedom obeys the Weyl equation, provided that we perform a simple relabeling of the coordinate axes or demand rotational symmetry in the continuum limit. It is surprising that this occurs regardless of the specific details of the evolution: it would be natural to assume that discrete evolutions giving rise to relativistic dynamics in the continuum limit would be very special cases. We also see that the same is not…
We revisit the classical theory of a relativistic massless charged point particle with spin and interacting with an external electromagnetic field. In particular, we give a proper definition of its kinetic energy and its total energy, the latter being conserved when the external field is stationary. We also write the conservation laws for the linear and angular momenta. Finally, we find that the particle's velocity may differ from $c$ as a result of the spin---electromagnetic field interaction, without jeopardizing Lorentz invariance.
We construct the vector fields associated to the space-time invariances of relativistic particle theory in flat Euclidean space-time. We show that the vector fields associated to the massive theory give rise to a differential operator realization of the Poincare algebra, while the vector fields associated to the massless theory, including the space-time supersymmetric sector, allow extensions of the conformal algebra in terms of commutators.
