The effective action of a spin 1/2 field in the background of a chiral soliton

We use a recently developed numerical technique in order to evaluate the renormalized effective action of a spin 1/2 field with a chiral mass term, the chiral angle being given by a static hedgehog configuration. The method is based on the use of Euclidean Green's functions. The divergent parts are regularized and renormalized analytically. For the sum over all convergent contributions we obtain an exact expression that can be evaluated numerically. A precarious numerical subtraction of the divergent parts is avoided by making use of integral equations for the partial waves.     

The soliton of the effective chiral action

The baryon-number-1 soliton solution of the effective chiral meson action of QCD is found numerically. For this purpose the underlying fermion determinant (quark loop) is calculated in a non-perturbative way by diagonalizing the corresponding Dirac hamiltonian. The vacuum energy is defined within a static version of the proper-time regularization. Topological soliton solutions are found for cut-offs below some critical value, above which only topologically trivial solutions exist.     

The soliton of the effective chiral action in a heat-kernel expansion

It is shown that the heat-kernel expansion (rather than the gradient expansion) of the effective chiral action of the quark loop yields in next-to-leading (i.e., fourth) order an effective low-energy lagrangian which possesses stable soliton solutions. The baryon number-one soliton solution of this effective chiral lagrangian is found numerically.     

Exact soliton solution of spin chain with an external magnetic field in linear wave background

Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.     

Abelian Ward identity from the background field dependence of the effective action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We show that for Abelian theories the Ward identity follows from the more general background field identity. This observation is relevant for the formulation of effective actions with an infrared cutoff since the solution of exact flow equations must obey an anomalous Ward identity.     

The effective two-loop Euler-Heisenberg action for scalar and spinor QED in a general constant background field

Using the Wordline formalism of QED we compute the two-loop effective action induced by a charged scalar, respectively spinor particle in a general constant electromagnetic field.     

Berry phase for a spin 1/2 particle in a classical fluctuating field

The effect of fluctuations in the classical control parameters on the Berry phase of a spin 1/2 interacting with an adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Induced effective action in 6D hypermultiplet theory on a vector/tensor background

We consider the six dimensional hypermultiplet, vector and tensor multiplet models in (1,0) harmonic superspace and discuss the corresponding superfield actions. Manifestly a (1,0) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contributions to the effective action is calculated.     

Ground state of a spin 1/2 charged particle in an even-dimensional magnetic field

We investigate the ground state structure of the Schrödinger operator (Pauli Hamiltonian)H with a magnetic fieldb for a spin 1/2 charged particle in ^{2d 2d d} . We consider the case whereb is given by the complex exterior derivative of a functionW on ^d of the form W. We find that dim kerH is related to the asymptotic behavior ofW at infinity. More precisely, if there exists a constantC such that there exists the nonzero limit lim_|z|e ^w(z) /|z|^–C , then dim kerH is equal to the number of all monomialsf ind variables such that the degree off is smaller than |C| -d. In the case whereC , under a weaker assumption this conclusion holds. Moreover, we clarify the structure of kerH.     

Note on the two inequivalent spin 1/2 baryon field operators

There are two inequivalent spin 1/2 local baryon field operators that can be constructed from 3 quarks. A priori theJ ^P =1/2⁺ baryons can couple to any linear combination of these operators. We show however that the coupling of the 1/2⁺ baryons to these operators is determined by the value of theSU(3) ratio ofF toD type pseudoscalar-baryon couplings. The experimental value of this ratio implies, for example, that the proton couples strongly to (u ^T C _γ d)u and weakly to (u ^T C d)γ _s u. This is of interest in QCD sum rule applications.     

The effective gauge field action of a system of non-relativistic electrons

We consider a system of free, non-relativistic electrons at zero temperature and positive density, coupled to an arbitrary, external electromagnetic vector potential,A. By integrating out the electron degrees of freedom we obtain the effective action forA. We show that, in the scaling limit, this effective action is quadratic inA and can be viewed as an integral over the Fermi sphere of effective actions of (1+1)-dimensional, chiral schwinger models. We use this result to elucidate Luther-Haldane bosonization of systems of non-relativistic electrons. We also study systems of weakly coupled interacting electrons for which the BCS channel is turned off. Using the quadratic dependence of the effective action onA, we show that, in the scaling limit, the RPA yields the dominant contribution.     

Stress-energy tensor for a massless spin 1/2 field in static black hole spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static nonrotating black holes, corresponding to the Schwarzschild, Reissner-Nordstr?m, and extreme Reissner-Nordstr?m solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress energy differs even in sign from the analytic approximation. For the Reissner-Nordstr?m and extreme Reissner-Nordstr?m solutions, divergences predicted by the analytic approximations are shown not to exist.     

Scaling behaviour of the effective chiral action and stability of the chiral soliton

The effective chiral action is evaluated within a novel improved heat-kernel expansion, which includes gradients of the chiral field in a non-perturbative way. This expansion is valid for both small and large momenta. The exact scaling behaviour of the effective action of a localized chiral field with respect to changing its spatial size is found. From this it is proved that the radiatively induced derivative terms cannot absolutely stabilize the chiral soliton against collapsing. The collapsing of the soliton is, however, accompanied by a vanishing of the baryon charge. It is argued that the effective chiral action constrained to a fixed baryon number may still admit stable soliton configurations.     

An effective action for a variable electromagnetic field

This work consists essentially of two parts. The first part is an analysis of the one-loop effective action using the zeta-function approach. This gives a simple expression for the effective action in terms of the background field propagator. The next-of-kin to the zeta-function, the heat kernel, is given in terms of B. DeWitt's proper time expansion (also known as P. B. Gilkey's theorem). It is calculated in the second part for fermions interacting with an external electromagnetic field to first nonvanishing order in the variations of the gauge field.     

The effect of Schwarzschild field on spin 1/2 particles compared to the effect of a uniformly accelerating frame

The Dirac Hamiltonian is calculated in the Schwarzschild space and compared to the analogous one in a uniformly accelerating Minkowski frame yielding a test of the equivalence principle. Comparing these Hamiltonians, we see that the flat-space energy-mass terms and their redshifted forms are the same in the two cases, but the coefficient of the spin-orbit coupling term is different and an additional term appears in the gravitational case.