We show that the on-shell effective theory (OSEFT) is the quantum field theory counterpart of a Foldy-Wouthuysen diagonalization of relativistic quantum mechanics for massless fermions. Thus, it is free of the Zitterbewegung oscillations that would yield an ill-defined meaning to the semiclassical transport approach at short distances if derived from the pure Dirac picture. We present a detailed derivation of the collision terms in the chiral kinetic theory using the OSEFT. Collision integrals are derived up to order 1/E, where E is the energy of an on-shell fermion. At this order, the collision terms depends on the spin tensor of the fermion, and in the presence of chiral imbalance, it describes how a massless fermion of a given helicity interacts differently with the transverse photons of different circular polarization. In order to back up our results, we check that they allow us to reproduce the fermion decay rate in an ultradegenerate plasma with a chiral imbalance computed directly from QED.
The phase space structure of zero temperature Quarkyonic Matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic Matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by m_Q = m_N/N_c, and N_c is the number of quark colors. The region of occupied states is for quarks k_Q < k_F/N_c, and for nucleons k_F < k_N < k_F + Δ. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core n…
We develop a method for constructing the Heavy Baryon Chiral Perturbation Theory Lagrangian (L_{HBChPT}), to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the nonrelativistic formalism. We obtain complete lists of independent terms in L_{HBChPT} through O(q^3) for off- shell nucleons. Then, eliminating equation-of-motion (eom) terms at the relativistic and no…
A quantum kinetic equation has been derived for the description of pair production in a time-dependent homogeneous electric field $E(t)$. As a source term, the Schwinger mechanism for particle creation is incorporated. Possible particle production due to collisions and collisional damping are neglected. The main result is a closed kinetic equation of the non-Markovian type. In the low density approximation, the source term is reduced to the leading part of the well known Schwinger formula for the probability of pair creation. We compare the formula obtained with other approaches and discuss th…
We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely man…
An extensive, growing body of work has been penned on cosmologies that include one or more sterile neutrinos. Early entries in the literature formulated a Boltzmann-like equation describing sterile-neutrino production in a way that bypasses the numerical tracking of high-frequency complex phases, and meticulous quantum-kinetic analyses shortly thereafter put the formula on firmer ground. A new and more direct derivation is given here, showing that the equation follows almost immediately from a quantum relaxation-time approximation and an expansion in the mixing angle. Besides reproducing the d…
derivation of the effective lagrangian for non-relativistic quantum chromodynamics and the heavy quarks effective field theory is given. Our calculation provides of a simple and systematic method of calculation of the full off shell effective lagrangian at tree level including all the $1/m$ corrections.
We construct a complete list of O(q^4) terms directly within Heavy Baryon Chiral Perturbation Theory (HBChPT) in the absence of external fields and assuming isospin symmetry. In addition to a phase rule recently developed (NPA646, 343, '99), a variety of algebraic identities and reparameterization invariance, are used to ensure linear independence of the terms and their low energy coupling constants. We first construct O(q^4) terms terms for off-shell nucleons, and then perform the on-shell reduction, again within HBChPT. We discuss an application of the O(q^4) terms to the evaluation of the O…
Using the iterative solution of Boltzmann equation in the relaxation-time approximation, the derivation of a third-order evolution equation for shear stress tensor is presented. To this end we first derive the expression for viscous corrections to the phase-space distribution function, $f(x,p)$, up to second-order in derivative expansion. The expression for $δf(x,p)$ obtained in this method does not lead to violation of the experimentally observed $1/\sqrt{m_T}$ scaling of the femtoscopic radii, as opposed to the widely used Grad's 14-moment approximation. Subsequently, we present the derivati…
We perform a systematic gradient expansion on kinetic equations and derive the CP-violating semiclassical force for fermions propagating in presence of a CP-violating wall at a first order electroweak phase transition. The force appears at order h-bar in the flow term of the kinetic equation and agrees with the semiclassical force used for baryogenesis computations. In particular we consider the force for charginos in both the MSSM and NMSSM. We then study the continuity equations for the vector and axial vector currents and stress the role of the latter as the one containing baryogenesis sour…
We present the derivation of a novel third-order hydrodynamic evolution equation for shear stress tensor from kinetic theory. Boltzmann equation with relaxation time approximation for the collision term is solved iteratively using Chapman-Enskog like expansion to obtain the nonequilibrium phase-space distribution function. Subsequently, the evolution equation for shear stress tensor is derived from its kinetic definition up-to third-order in gradients. We quantify the significance of the new derivation within one-dimensional scaling expansion and demonstrate that the results obtained using thi…
In these proceedings we discuss the relation between the kinetic and the on-shell schemes for the bottom and the charm quarks and present the methods for the calculation of the mass relation to higher orders in perturbative QCD. The bottom mass in the kinetic scheme is a pivotal input parameter in the inclusive determination of $|V_{cb}|$ from $B\to X_c \ell ν_\ell$ decays. By combining the relation between the kinetic and the on-shell mass with well-know results for the $\overline{\mathrm{MS}}$-on-shell conversion, we obtain a prediction for $m_b^\mathrm{kin}$ based on precise determinations …
We extend the kinetic theory of $D$ mesons to accommodate thermal and off-shell effects due to the medium modification of the heavy-meson spectral functions. From the Kadanoff-Baym approach we derive the off-shell Fokker-Planck equation which encodes the heavy-flavor transport coefficients. We analyze the thermal width (damping rate) of $D$ mesons due to their scattering off light mesons, focusing on new in-medium effects: off-shell corrections, inelastic channels, and the contribution of the Landau cut. We obtain that the latter effect (absent for vacuum scattering amplitudes) brings sizable …
We present a nonperturbative derivation of effective valence-shell Hamiltonians in the framework of the recently developed in-medium similarity renormalization group (IM-SRG). As a first application, we calculate the spectra of $p$- and $sd$-shell nuclei, $^6$Li and $^{18}$O, based on evolved chiral nucleon-nucleon interactions. For $^6$Li, the spectrum is in very good agreement with ab-initio results. For $^{18}$O, the IM-SRG provides a new method for the shell model to systematically go beyond effective interaction techniques based on diagrammatic expansions.
We formulate the on-shell effective field theory (OSEFT) in an arbitrary frame and study its reparametrization invariance (RI), which ensures that it is respectful of Lorentz symmetry. In this formulation the OSEFT Lagrangian looks formally equivalent to the sum over light-like velocities of soft collinear effective field theory in the Abelian limit, differences remain in the scale of the gauge fields involved in the two effective theories. We then use the OSEFT Lagrangian expanded in powers of the on-shell energy to derive how the classical transport equations for charged massless fermions ar…
A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic ab…
In this thesis we develop a novel approximation scheme (eQPA), where the effects of nonlocal coherence are included in the kinetic approach to nonequilibrium quantum dynamics. The key element in our formalism is the finding of new singular shell solutions, located at $k_{0,z} = 0$ in the phase space of 2-point Wightman function, which describe the nonlocal quantum coherence between the ``opposite'' mass-shell excitations for spatially homogeneous and static planar symmetric problems, respectively. This phase space structure leads to a closed set of transport equations for the corresponding on-…
We investigate quantum kinetic theory for a massive fermion system under a rotational field. From the Dirac equation in curved space we derive the complete set of kinetic equations for the spin components of the covariant and equal-time Wigner functions. While the particles are no longer on a mass shell in general case due to the rotation-spin coupling, there are always only two independent components, which can be taken as the number and spin densities. With the help from the off-shell constraint we obtain the closed transport equations for the two independent components in classical limit an…
We study the dynamics of relaxation and thermalization in an exactly solvable model with the goal of understanding the effects of off-shell processes. The focus is to compare the exact evolution of the distribution function with different approximations to the relaxational dynamics: Boltzmann, non-Markovian and Markovian quantum kinetics. The time evolution of the distribution function is evaluated exactly using two methods: time evolution of an initially prepared density matrix and by solving the Heisenberg equations of motion. There are two different cases that are studied in detail: i) no s…
In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are non-singular in $\varepsilon = p^2 - m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.
