On quantum electrodynamics of two-particle bound states containing spinless particles

We develop here the general treatment arising from the Bethe-Salpeter equation for a two-particle bound system in which at least one of the particles is spinless. It is shown that a natural two-component formalism can be formulated for describing the propagators of scalar particles. This leads to a formulation of the Bethe-Salpeter equation in a form very reminiscent of the fermion-fermion case. It is also shown, that using this two-component formulation for spinless particles, the perturbation theory can be systematically developed in a manner similar to that of fermions. Quantum electrodynamics for scalar particles is then developed in the two component formalism, and the problem of bound states, in which one of the constituent particles is spinless, is examined by means of the means of the Bethe-Salpeter equation. For this case, the Bethe-Salpeter equation is cast into a form which is convenient to perform a Foldy-Woutyhuysen transformation which we carry out, keeping the lowest-order relativistic corrections to the nonrelativistic equation. The results are compared with the corresponding fermion-fermion case. It is shown, as might have been expected, that the only spin-independent terms that occur for the fermion-fermion system which do not occur for bound scalar particle cases, is the zitterbewegung contribution. The relevance of the above considerations for systems that are essentially bound by electromagnetic interactions, such as kaonic hydrogen, is discussed.     

Two-Point Function Reduction of Four-Point Amputated Functions and Transformations in FF and RA Basis in a Real-Time Finite Temperature NJL Model

Based on a general analysis of Green functions in the real-time thermal field theory, we have proven that the four-point amputated functions in an NJL model in the fermion bubble diagram approximation behave like usual two-point functions. We expound the thermal transformations of the matrix propagators for a scalar bound state in the FF basis and in the RA basis respectively. The resulting physical causal, advanced and retarded propagators are respectively identical to corresponding ones derived in the imaginary-time formalism, and this shows once again the complete equivalence of the two formalisms of thermal field theory on the discussed problem in the NJL model.     

Explicit Proof of Equivalence of Two—Point Functions in the Two Formalisms of Thermal Field Theory

We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal λφ^3 theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories,including the one of the propagators for scalar bound states in an NJL model.     

Real-Time Thermal Field Theory Analyses of 2D Gross-Neveu Model

The discrete symmetry breaking and possible restoration at finite temperature T are analyzed in 20 Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass m is proven to, be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the meanfield approximation used in the auxiliary scalar field approach. Reproducing of the nonzero critical temperature T_c = 0.567m(O), m(0) is the dynamical fermion mass at T = 0, shows the equivalence between the real-time and the imaginary-time thermal. field theories in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the ln(T_c/T) behavior of m² at T ≤ T_c can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.     

Selfconsistent calculations of hadrons at finite temperature

A set of selfconsistent Schwinger-Dyson equations for the Walecka model is derived within the framework of the Cornwall-Jackiw-Tomboulis formalism. In the Hartree approximation these equations are solved by propagators with T- and μ-dependent masses. The results are compared to tree-level calculations. The difference is most pronounced for the mass of the scalar meson.     

Scalar meson spectroscopy with a fine lattice

With sufficiently light u and d quarks the isovector (a₀) and isosinglet (f₀) scalar meson propagators are dominated at large distances by two-meson states. In the staggered fermion formulation of lattice QCD, taste-symmetry breaking causes a proliferation of multihadron states that complicates the analysis of these channels. Of special interest is the bubble contribution, which makes a considerable contribution to these channels. Using numerical simulation we have measured the correlators for both a₀ and f₀ channels in the “Asqtad” improved staggered fermion formulation in a MILC fine (a=0.09 fm) lattice ensemble. We analyze those correlators using rooted staggered chiral perturbation theory (rSχPT) and achieve chiral couplings that are well consistent with previous determinations.     

Relativistic Shifted-l Expansion Technique for Dirac and Klein-Gordon Equations

The shifted-l expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or kvector potentials. A parameter λ = 0, l is introduced in such a way that one can obtain the Klein-Gordon (KG) bound states from Dirac bound states. The 4-vector Coulomb, the scalar linear, and the equally mixed scalar and 4-vector power-law potentials are used in KG and Dirac equations. Exact numerical results are obtained for the Cvector Coulomb potential in both KG and Dirac equations. Highly accurate and fast converging results are obtained for the scalar linear and the equally mixed scalar and 4-vector power-law potentials.     

Upper and Lower Bound States for Zero Dimensional Space in Scalar Quantum Field Theory

International Journal of Theoretical Physics - The varational method with the Hamiltonian formalism of quantum field theory (QFT) is used to study the bound state for scalar particle and...     

One-loop renormalizability of noncommutative U(1) gaugetheory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propagators in noncommutative U(1) gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to θ²-order, but for a massive scalar field they are renormalizable only to θ-order.     

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin–Kemmer–Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff–Snyder–Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles.     

Excited states of bosons and fermions in a four-Fermi quantum field theory

A scalar-pseudoscalar four-Fermi quantum field model in four dimensional space-time is considered. Introducing the scalar and pseudoscalar collective bosons, the path-integral representation for the generating functional for Green's functions in terms of the effective total action integral containing only collective bosons is expressed. Using a classcal ground-state solution for collective bosons, a new formula for the generating functional for collective boson and fermion Green functions in terms of the effective propagators is derived. It is shown by a partly nonperturbative analysis that the excited states of collective bosons do exist and form finite trajectories in the plane mass-square-spin. These trajectories for bosons are approximately linear in J, as the experimental trajectories. The existence of fermion bound or excited states depend on the value of the dynamical parameters of the model. For some values of dynamical parameters there are bound states for $\text{J =}\text{1}\text{2}$ and $\text{3}\text{2}$. However, for most of other values bound or excited fermion states do not exist.     

Scattering and bound states of spinless particles in a mixed vector–scalar smooth step potential

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schrödinger-like equation with an effective Rosen–Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and more efficient problem of solving an irrational algebraic equation.     

Bound states of scalar and spinor particles with arbitrary isospin in the regular Dyon field

The problem of bound states of the spinor and scalar particles with arbitrary isospin on the back-ground of regular magnetic monopole and dyon solution of theSU(2) gauge system is considered using Newman-Penrose formalism. The explicit general formulas for the energy eigenvalues are obtained which are in agreement with many particular cases described earlier.     

Energy levels of a scalar particle in a static gravitational field close to the black hole limit

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.     

Time-dependent variational principle for quantum lattices

We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary-time dynamics for infinite one-dimensional quantum lattices. This procedure (i) is argued to be optimal, (ii) does not rely on the Trotter decomposition and thus has no Trotter error, (iii) preserves all symmetries and conservation laws, and (iv) has low computational complexity. The algorithm is illustrated by using both an imaginary-time and a real-time example.     

Continuous Quantum Nondemolition Measurements of a Particle in Electromagnetic and Gravitational Fields

The detection of a particle in electromagnetic plus gravitational fields is investigated. We obtain a set of quantum nondemolition variables. The continuous measurements of these nondemolition parameters are analyzed in the framework of restricted path integral formalism. We manipulate the corresponding propagators, and deduce the probabilities associated with the possible measurement outputs.     

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.     

Creation of Dirac particles in general relativity with torsion and electromagnetism I: The general formalism

Generalizing a formalism developed earlier for the scalar field, we propose a covariant quantization procedure for the Dirac field coupled to external gauge fields. Under the assumption of a very natural spectrum condition, physical in and out states are identified by certain analyticity properties in the mass parameter. Several criteria for particle creation are given.     

Continuous Quantum Nondemolition Measurements of a Particle in Electromagnetic and Gravitational Fields

The detection of a particle in electromagnetic plus gravitational fields is investigated. We obtain a set of quantum nondemolition variables. The continuous measurements of these nondemolition parameters are analyzed in the framework of restricted path integral formalism. We manipulate the corresponding propagators, and deduce the probabilities associated with the possible measurement outputs.     

Hard thermal loops in a gravitational field

We calculate the high-temperature (T ⁴) limit of the 3-graviton vertex function, with a single loop of internal scalar particles in thermal equilibrium. We use the analytically continued imaginary-time formalism. We verify a particular case of the Ward identity connecting the 3- and 2-graviton functions. This confirms that there is covariance under general coordinate transformations (which reduce to the identity at infinity). We remark that the ghost-ghost-graviton vertex (with ghost and graviton internal lines) has noT ⁴ term. This implies that the 3-graviton function with internal graviton (and ghost) lines must satisfy the Ward identity too, so it is possible for it to be proportional to the scalar contribution. We have verified this for that part of the vertex function which is manifestly symmetric and traceless in the six Lorentz indices.