arXiv subjects

H. Arthur Weldon

Publications and source records attributed to H. Arthur Weldon.

At least 19 recordsLinked to original sources

arXiv2024

The Tolman-Ehrenfest effect for an ideal gas in a background of time-independent electric, magnetic, and gravitational fields

The statistical mechanics of an ideal gas of point particles moving in a time independent background metric with $g_{0j}\neq 0$ is investigated. An explicit calculation shows that when there is no background electrostatic or magnetostatic field the thermodynamic pressure, energy density, and thermally averaged energy-momentum tensor depend on temperature and chemical potential only through the ratios $T_{0}/\sqrt{g_{00}}$ and $μ_{0}/\sqrt{g_{00}}$. A background magnetostatic field does not change this, however with a background electrostatic field the previous results are multiplied by a factor $\exp(-eA_{0}/T_{0})$, which is an exception to the strict Tolman-Ehrenfest rule because the system is open.

hep-th↗

arXiv2023

Equality of the Hilbert Hamiltonian and the canonical Hamiltonian for gauge theories in a static spacetime

The Hilbert energy-momentum tensor for gauge-fixed non-Abelian gauge theories, defined by the variational derivative of the action with respect to the space-time metric, is a tensor under general coordinate transformations, symmetric in its indices, and BRST invariant. The canonical energy-momentum tensor has none of these properties but the canonical Hamiltonian does correctly generate the time dependence of the fields. It is shown that the Hilbert Hamiltonian $\int d^{3}x\,\sqrt{g}\;T^{0}_{\;\; 0}$ is equal to the canonical Hamiltonian for a general gauge theory coupled to spin 1/2 and spin 0 matter fields (including an $Rϕ^{2}$ term) in a static background metric ($\partial_{0}g_{μν}=0$ and $g_{0j}=0$). The equality depends on on the Gauss's law constraint but not on the dynamical Euler-Lagrange equations.

hep-th↗

arXiv2022

Pressure-Strain Interaction: II. Decomposition in Magnetic Field-Aligned Coordinates

In weakly collisional and collisionless magnetized plasmas, the pressure-strain interaction describes the rate of conversion between bulk flow and thermal energy density. In this study, we derive an analytical expression for the pressure-strain interaction in a coordinate system with an axis aligned with the local magnetic field. The result is eight groups of terms corresponding to different physical mechanisms that can contribute to the pressure-strain interaction. We provide a physical description of each term. The results are immediately of interest to weakly collisional and collisionless magnetized plasmas and the fundamental processes that happen therein, including magnetic reconnection, magnetized plasma turbulence, and collisionless shocks. The terms in the field-aligned coordinate decomposition are likely accessible to measurement with satellite observations.

physics.plasm-ph↗

arXiv2022

Thermodynamic pressure for massless QCD and the trace anomaly

From statistical mechanics the trace of the thermal average of any energy-momentum tensor is $\langle T^μ_{\;\;μ}\rangle =T\partial P/\partial T-4P$. The renormalization group formula $\langle T^μ_{\;\;μ}\rangle =β(g_{M})\partial P/\partial g_{M}$ for QCD with massless fermions requires the pressure to have the structure \begin{equation} P=T^{4}\sum_{n=0}^{\infty} ϕ_{n}(g_{M})\big[\ln\big({M\over 4πT}\big)\big]^{n},\end{equation} where the factor $4π$ is for later convenience. The functions $ϕ_{n}(g_{M})$ for $n\ge 1$ may be calculated from $ϕ_{0}(g_{M})$ using the recursion relation $n\,ϕ_{n}(g_{M})=-β(g_{M})dϕ_{n-1}/dg_{M}$. This is checked against known perturbation theory results by using the terms of order $(g_{M})^{2}, (g_{M})^{3}$, $(g_{M})^{4}$ in $ϕ_{0}(g_{M})$ to obtain the known terms of order $(g_{M})^{4}, (g_{M})^{5}$, $(g_{M})^{6}$ in $ϕ_{1}(g_{M})$ and the known term of order $(g_{M})^{6}$ in $ϕ_{2}(g_{M})$. The above series may be summed and gives the same result as choosing $M=4πT$, viz. $T^{4}ϕ_{0}(g_{4πT})$.

hep-th↗

arXiv2004

Search for Combinations of Thermal n-point Functions with Analytic Extensions

The 2^{n} different n-point functions that occur in real-time thermal field theory are Fourier transformed to real energies. Because of branch cuts in various energy variables, none of these functions can be extended analytically to complex energies. The known linear combinations that form the fully retarded and advanced functions can be extended analytically. It is proven that no other linear combinations have an analytic extension to complex energies.

hep-ph↗

arXiv2003

The electron thermal propagator at p>>T: An entire function of p_{0}

The retarded electron propagator S_{R}(p_{0},p) at high momentum p>>T was shown by Blaizot and Iancu to be an entire function of complex p_{0}. In this paper a specific form for S_{R}(p_{0},p) is obtained and checked by showing that its temporal Fourier transform S_{R}(t, p) has the correct behavior at large t. Potential infrared and collinear divergences from the emission of soft photons do not occur.

hep-ph↗

arXiv2003

Thermal Self-Energies Using Light-Front Quantization

A recent paper by Alves, Das, and Perez contains a calculation of the one-loop self-energy in ϕ^{3} field theory at T\neq 0 using light-front quantization and concludes that the self-energy is different than the conventional answer and is not rotationally invariant. The changes of variables displayed below show that despite the complicated appearance of the thermal self-energy in light-front variables, it is exactly the same as the conventional result.

hep-ph↗

arXiv2003

Thermal Field Theory and Generalized Light Front Coordinates

The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general coordinates the metric tensor $g_{\bar{μν}}$ is non-diagonal. The Kubo, Martin, Schwinger condition requires periodicity in thermal correlation functions when the temporal variable changes by an amount $-i\big/(T\sqrt{g_{\bar{00}}})$. Light front quantization fails since $g_{\bar{00}}=0$, however various related quantizations are possible.

hep-ph↗

arXiv2002

Analytic Properties of Finite-Temperature Self-Energies

The analytic properties in the energy variable k_{0} of finite-temperature self-energies are investigated. A typical branch cut results from n particles being emitted into the heat bath and n' being absorbed from the heat bath. There are three main results: First, in addition to the branch points at which the cuts terminate, there are also branch points attached to the cuts along their length. Second, branch points at k_{0}=\pm k are ubiquitous and for massive particles they are essential singularities. Third, in a perturbative expansion using free particle propagators or in a resummed expansion in which the propagator pole occurs at a real energy, the self-energy will have a branch point at the pole location.

hep-ph↗

arXiv2000

Fermions without Vierbeins in Curved Space-Time

A general formulation of spinor fields in Riemannian space-time is given without using vierbeins. The space-time dependence of the Dirac matrices required by the anticommutation relation {γ_μ,γ_ν}=2g_{μν} determines the spin connection. The action is invariant under any local spin base transformations in the 32 parameter group Gl(4,c) and not just under local Lorentz transformations. The Dirac equation and the energy-momentum tensor are computed from the action.

gr-qc↗

arXiv2000

Asymptotic Space-Time Behavior of HTL Gauge Propagator

The asymptotic behavior as t\to\infty and r\to\infty of the hard-thermal-loop propagator D^{μν}(t,r) is computed in the Coulomb gauge. The asymptotic falloff is always a power law though generally different in the deep time-like and space-like regions. The contributions of quasiparticle poles and Landau branch cuts are computed. The most difficult calculation is the contribution of the branch cut in the transverse propagator D^{ij}(t,r). For QED this produces a leading behavior of order T/r in both the time-like and space-like regions. The inclusion of a magnetic mass so as to describe QCD makes the leading behavior 1/(Tr^{3}), thus improving the infrared convergence. The asymptotic space-like behavior of all contributions (longitudinal and transverse, poles and cuts) is confirmed by also computing in the Euclidean formalism and analytically continuing. The results are compared will those for free gauge bosons at finite temperature.

hep-ph↗

arXiv2000

Thermal Green Functions in Coordinate Space for Massless Particles of any Spin

The thermal Wightman functions for free, massless particles of spin 0, 1/2, 1, 3/2, and 2 are computed directly in coordinate space by solving the appropriate differential equation and imposing the Kubo-Martin-Schwinger condition. The solutions are valid for real, imaginary, or complex time. The Wightman functions for spin 1 gauge bosons and for spin 2 gravitons are directly related to the fundamental functions for spin 0. The Wightman functions for spin 3/2 gravitinos is directly related to that for spin 1/2 fermions. Calculations for spin 1, 3/2, and 2 are done in covariant gauges. In the deep space-like region the Wightman functions for bosons fall like $T/r$ whereas those for the fermions fall exponentially. In the deep time-like region all the Wightman functions fall exponentially.

hep-ph↗

arXiv2000

Green Functions in Coordinate Space for Gauge Bosons at Finite Temperature

The thermal Green function $D^{μν}(x)$ for free, massless gauge bosons is computed exactly in a variety of gauges (Feynman, covariant, Coulomb, and Landshoff-Rebhan). At large temporal separations it falls exponentially. At large spatial separations it falls like $T/r$. In contrast, the zero-temperature propagator falls quadratically in both regimes, being proportional to $1/x^{2}$.

hep-ph↗

arXiv1999

Structure of the Quark Propagator at High Temperature

In the high temperature, chirally invariant phase of QCD, the quark propagator is shown to have two sets of poles with different dispersion relations. A reflection property in momentum space relates all derivatives at zero-momentum of the particle and hole energies, the particle and hole damping rates, and the particle and hole residues. No use is made of perturbation theory.

hep-ph↗

arXiv1998

Quasiparticles in Finite-Temperature Field Theory

Conventional finite-temperature perturbation theory in which propagators have poles at $k^{2}=m^{2}$ is shown to break down at the two-loop level for self-interacting scalar fields. The breakdown is avoided by using free thermal propagators that have poles at the same energy as the exact thermal propagator. This quasiparticle energy ${\cal E}(\vec{k})$ is temperature-dependent, complex, and gauge invariant. An operator theory containing two self-adjoint scalar fields is presented in which all temperature dependence is incorporated into the Hamiltonian. No thermal traces are required to compute thermal Green functions. Choosing the spectrum of the unperturbed part of the Hamiltonian to contain the exact quasiparticle energy ${\cal E}(\vec{k})$ produces a resummed perturbation theory that has the correct poles and branch cuts. The location of the poles and cuts is explained directly in terms of the spectrum of the Hamiltonian.

hep-ph↗

arXiv1998

Mass-Shell Behavior of Electron Propagator at Low Temperature

At T=0 the full electron propagator is known to have an infrared anomalous dimension and thus a branch point at $P^{2}=m^{2}$ rather than a pole. An explicit calculation shows that if $0<eT\ll m$ the retarded self-energy is analytic in the vicinity of $P^{2}\approx m^{2}$, which includes the thermal mass-shell. The low-temperature propagator has a simple pole. Only when T=0 is there a branch point at the mass-shell.

hep-ph↗

arXiv1998

Energy and momentum density of thermal gluon oscillations

In the exact propagator for finite temperature gluons the location of the transverse and longitudinal poles in the gluon propagator are unknown functions of wave vector: $ω_{T}(k)$ and $ω_{L}(k)$. The residues of the poles, also unknown, fix the normalization of the one gluon vector potential and thus of the field strength. The naive energy density $\pol{E}\cdot\pol{D}+\pol{B}\cdot\pol{H}$ is not correct because of dispersion. By keeping the modulations due to the source currents the energy density is shown to be $ω_{T}/V$ and $ω_{L}/V$ regardless of the functional form of $ω_{T}(k)$ and $ω_{L}(k)$. The momentum density is $k/V$. The resulting energy-momentum tensor is not symmetric.

hep-ph↗

arXiv1998

New Mesons in the Chirally Symmetric Plasma

A nonperturbative proof is given that the chirally-invariant quark propagator contains both particle and hole singularities with different dispersion relations. Mesons made of a quark and a hole will produce dilepton pairs at masses characteristic of the plasma and with a distinct energy dependence.

hep-ph↗