arXiv subjects
Publications and source records attributed to Ernst Trojan.
We solve the equations of motion and find the Lorentz transformation associated with a kink in superconducting cosmic string. The kink velocity does not depend on its amplitude. The kink amplitude cannot be arbitrary but it varies within definite range and determines the explicit form of the relevant Lorentz transformation.
We formulate an analytic method to study the discontinuities in superconducting cosmic strings. Equations of discontinuities and conditions of their existence are derived from the intrinsic and extrinsic equations of motion. It is the fundamental for research of particular solutions, associated with kinks, cusps and shocks.
In a paper appearing in this issue of Physical Review D, Burmistrov raises some critical comments on the thermodynamics of a cold tachyon Fermi gas [E. Trojan and G. V. Vlasov, Phys. Rev. D 83, 124013 (2011)]. However, apart from any possible theoretical speculation, there are the basic physical principles to test the theory.
Superconducting cosmic string may admit shock-like discontinuities of the current when the latter is spacelike ("magnetic" regime), while no shock at timelike current ("electric" regime) was discovered in numerical simulations. We find that the necessary and enough conditions for existence of stable shocks and show that the shock can be unstable in the presence of infinitesimal extrinsic perturbations of the string worldsheet. The shocks in the "magnetic" regime are not vulnerable to this instability but the shocks in the "electric" regime do not survive.
Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term χ. The hypersurface of discontinuity propagates at finite velocity determined by finite increment Δχ=χ_+ -χ_-. The current increases χ_+>χ_- in stable shocks but transition between spacelike (χ>0) and timelike (χ<0) currents is impossible.
A consistent description of charged many-tachyon Fermi system is developed. Tachyons and antitachyons have the same chemical potential μ+=μ- because the axial coupling constant g+=g- is invariant under the charge conjugation, in contrast to reversion of the electric charge e+=-e-. The axial density n5=<ψ^ γ5 ψ> is incorporated in the thermodynamical functions instead of <ψ^ ψ> which is not associated with any conserved quantity. The number of tachyons and antitachyons are undefined but it is possible to estimate their difference and establish a link between the total electric charge density $en$ and $n5$.
We consider a system of many fermions with tachyonic energy spectrum \varepsilon_k=\sqrt{k^2-m^2} and clarify that tachyons with imaginary energy and low momentum (k<m) play the role of Dirac sea in a many-tachyon Fermi system and make contribution to the thermodynamical functions. The energy and pressure acquire additional constant terms that, however, is not reflected in the sound speed. Replacement $m=im$ results in the thermodynamical functions and the sound speed of an ordinary Fermi gas. When the Fermi momentum approaches the Dirac sea level k_F=m, the group velocity of most tachyons above the sea is unbound, while the sound speed tends to infinity. This scenario is not encountered in practice because the cold tachyon Fermi gas becomes unstable with respect to hydrodynamical perturbations when k_F<\sqrt{3/2}m. The particle number density of a stable many-tachyon system is always finite and exceeds the critical value depending on the tachyon mass m.
We consider a system of many fermionic tachyons coupled to a scalar, pseudoscalar, vector and pseudovector fields. The scalar and pseudoscalar fields are responsible for the effective mass, while the pseudovector field is similar to ordinary electromagnetic field. The action of vector field $ω_μ$ results in tachyonic dispersion relation $\varepsilon_p=\sqrt{p^2+g^2ω_0^2-hpgω_0-g\vec σ\cdot \nabla ω_0-m^2} -g\vec σ\cdot \vec ω$ that depends on helicity $h$ and spin $\vec σ$. We apply the mean field approximation and find that there appears a vector condensate with finite average $<ω_0>$ depending on the tachyon density. The pressure and energy density of a many-tachyon system include the mean-field energy $<\varepsilon_p> =\sqrt{p^2+hpng^2/M^2+n^2g^4/M^4-m^2}$ which is real when the particle number density exceeds definite threshold which is $n>mM^2/g^2$ for right-handed and $n>\frac 2{\sqrt{3}}mM^2/g^2$ for left-handed tachyons, while all tachyons are subluminal at high density. There is visible difference in the properties of right-handed and left-handed tachyons. Interaction via the vector field $ω_0$ may lead to stabilization of tachyon matter if its density is large enough.
The effect of nonlinear self-interaction can be associated with superluminal velocity of neutrino. The power energy spectrum E=p+Cp^a is derived from the nonlinear Dirac equation when interaction term V=λ(ψγ_μψψγ^μψ)^a is added to the Lagrangian of a free spin-1/2 particle. The superluminal velocity recorded by the OPERA and MINOS collaborations is achieved when the coupling constants are taken in the range a=0.4-1.18 and λ=-(0.5-1.6)x10^-4. The self-interaction Lagrangian V=λ(ψγ_μψψγ^μψ) with the coupling constant λ=-(0.7-0.9)x10^-4 yields the same result. Scalar interaction V=λ(ψψ)^b and scalar-vector interaction λ(ψ^{+}ψ)^{b+1}/(ψψ)^b cannot be responsible for the observed superluminal neutrino.
We analyze the velocity dependence on energy of superluminal neutrino recorded by the OPERA and MINOS collaborations and manage to approximate the energy spectrum by a power law E=p+Cp^a where parameters must be taken in the range a=0.40--1.18 and C=1.5x10^{-5}--4.15x10^{-4} (momentum and energy are expressed in GeV). This rough estimation is constrained by the errors of measurements, and new experimental data are requested.
We consider a self-gravitating body composed of ideal Fermi gas of tachyons at zero temperature. The Oppenheimer-Volkoff equation is solved for various central densities and various tachyon mass parameter $m$. Although a pure tachyon star has finite mass, it cannot occur in nature because the equilibrium condition P=0 and the causality condition cannot be satisfied simultaneously. A stable configuration with tachyon content must be covered with a non-tachyon envelope. The boundary between the tachyon core and the envelope is determined by the critical pressure $P_T$, which depends on the tachyon mass $m$. The tachyon core is dominant and its mass can exceed many times the solar mass $M_{\odot}$ when $m$ is much smaller than the nucleon mass $m_p$, while at large $m$ compared with $m_p$, the main contribution to the total stellar mass is due to the envelope whose material determines the parameters of the whole star. However, the parameters of the tachyon core do not depend on the envelope material. When the tachyon core appears, its mass $M_T$ and radius $r_T$ grow up with increasing central density until maximum values are reached, after which the mass and radius slowly decrease. The redshift at the surface of the tachyon core does not depend on $m$ and never exceeds $z_{\max}\simeq 0.3$. The maximum mass of tachyon core and its maximum radius are achieved at certain central density and obey universal formulas $M_{T\max}/M_{\odot}=0.52m_p^2/m^2$ and $r_{T\max}=4.07m_p^2/m^2$ [km] that allow to estimate arbitrary supermassive tachyonic bodies at the cosmological scale.
We consider an ideal Fermi gas of tachyonic thermal excitations as a continuous medium and establish when it satisfies the causality condition. At high temperature the sound speed is always subluminal $c_s<1$, but there is no stable form of tachyon matter below the critical temperature $T_c<0.23m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but $P$ can exceed $E$, and $P=2.36E$ when $T\rightarrow T_c$.
The 'absolute stiff' matter ($P=E$) can be a Fermi or Bose gas of particles with the energy spectrum $ε_p \sim p^q$ in $q$-dimensional space, particularly $ε_p =p^3/m^2$ in 3-dimensional space. We obtain its pressure, particle number density and heat capacity at finite temperature. The behavior of 'absolute stiff' medium is determined by characteristic temperature $T_c=6π^2n/(γm^2)$. At low temperature the heat capacity obeys the linear law $C_V\sim T$ for both fermionic and bosonic matter, the pressure of 'absolute stiff' fermions $P\sim n^2+O(T^2)$, while the 'absolute stiff' Bose gas never reveals Bose-Einstein condensation.
We analyze several approaches to the thermodynamics of tachyon matter. The energy spectrum of tachyons $ε_k=\sqrt{k^2-m^2}$ is defined at $k\geq m$ and it is not evident how to determine the tachyonic distribution function and calculate its thermodynamical parameters. Integrations within the range $k\in (m,\infty) $ yields no imaginary quantities and tachyonic thermodynamical functions at zero temperature satisfy the third law of thermodynamics. It is due to an anomalous term added to the pressure. This approach seems to be correct, however, exact analysis shows that the entropy may become negative at finite temperature. The only right choice is to perform integration within the range $k\in (0,\infty) $, taking extended distribution function $f_ε=1$ and the energy spectrum $ε_k=0$ when $k<m$. No imaginary quantity appears and the entropy reveals good behavior. The anomalous pressure of tachyons vanishes but this concept may play very important role in the thermodynamics of other forms of exotic matter.
We consider a tachyon gas that obeys Maxwell-Boltzmann statistics. The sound speed is always subluminal and it tends to the limiting minimum value $c_s=1/\sqrt{2}$ in non-relativistic gas (at low temperature), decreasing monotonously with the growth of temperature and attaining ultra-relativistic limit $c_s=1/% \sqrt{3}$ at high temperature. The hot tachyon gas always satisfies the causality.
We consider an ideal Fermi gas of tachyons and derive a low temperature expansion of its thermodynamical functions. The tachyonic specific heat is linear dependent on temperature $C_V=ε_Fk_FT$ and formally coincides with the specific heat of electron gas if the tachyon Fermi energy is defined as $ε_F=\sqrt{k_F-m^2}$.
A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are not fully independent. The interaction between particles is reflected only in the equation of state of each component, but it deals nothing with the coupling between the fluid components and does not influence the hydrodynamic motion. A general form of two-fluid decomposition is formulated for arbitrary interacting system.
We consider a substance with equation of state $P=wE$ at constant $w$ and find that it is an ideal gas of quasi-particles with the energy spectrum $ε_p\sim p^{wq}$ that can constitute either regular matter (when $w>0$) or exotic matter (when $w<0$) in a $q$-dimensional space. Particularly, an ideal gas of fermions or bosons with the energy spectrum $ε_p=m^4/p^3$ in 3-dimensional space will have the pressure $P=-E$. Exotic material, associated with the dark energy at $E+P<0$, is also included in analysis. We determine the properties of regular and exotic ideal Fermi gas at zero temperature and derive a low-temperature expansion of its thermodynamical functions at finite temperature. The Fermi level of exotic matter is shifted below the Fermi energy at zero temperature, while the Fermi level of regular matter is always above it. The heat capacity of any fermionic substance is always linear dependent on temperature, but exotic matter has negative entropy and negative heat capacity.