880 research outputs found
Relaxing Lorentz invariance in general perturbative anomalies
We analyze the role of Lorentz symmetry in the perturbative non-gravitational
anomalies for a single family of fermions. The theory is assumed to be
translational invariant, power-counting renormalizable and based on a local
action, but is allowed to have general Lorentz violating operators. We study
the conservation of global and gauge currents associate with general internal
symmetry groups and find, by using a perturbative approach, that Lorentz
symmetry does not participate in the clash of symmetries that leads to the
anomalies. We first analyze the triangle graphs and prove that there are
regulators for which the anomalous part of the Ward identities exactly
reproduces the Lorentz invariant case. Then we show, by means of a regulator
independent argument, that the anomaly cancellation conditions derived in
Lorentz invariant theories remain necessary ingredients for anomaly freedom.Comment: 18 pages, 1 figure. Few comments added. Article published in Physical
Review
Singularities of Scattering Amplitudes on Unphysical Sheets and Their Interpretation
The analytic structure of two-particle scattering amplitudes on the unphysical sheet of the Riemann surface reached by crossing the two-particle cut is discussed. The singularities of the amplitudes there are shown to be poles and their physical interpretation is studied. The way in which bound states appear on the physical sheet in the Mandelstam representation, both as isolated poles and as cuts, is traced in detail. The properties of partial wave amplitudes and of the full amplitude as a function of energy and angle and of energy and momentum transfer are discussed. Finally, a few remarks are made in connection with unstable states
Effects of an extra U(1) axial condensate on the strong decays of pseudoscalar mesons
We consider a scenario (supported by some lattice results) in which a
U(1)-breaking condensate survives across the chiral transition in QCD. This
scenario has important consequences for the pseudoscalar-meson sector, which
can be studied using an effective Lagrangian model. In particular, generalizing
the results obtained in two previous papers, where the effects on the radiative
decays eta,eta' --> gamma gamma were studied, in this paper we study the
effects of the U(1) chiral condensate on the strong decays of the "light"
pseudoscalar mesons, i.e., eta,eta' --> 3pi^0; eta,eta' --> pi^+ pi^- pi^0;
eta' --> eta pi^0 pi^0; eta' --> eta pi^+ pi^-; and also on the strong decays
of an exotic ("heavy") SU(3)-singlet pseudoscalar state eta_X, predicted by the
model.Comment: One misprint in Eq. (2.10) has been eliminated; Eqs. (B.8) and (B.9)
in Appendix B have been corrected; 46 pages, 1 tabl
A soluble problem in dispersion theory
The Lee model is modified by addition of a new field θ′ and a weak coupling N+θ→N+θ′, which leads to instability of the V particle: V→N+θ→N+θ′. The decay amplitude is calculated to lowest order in the weak coupling by dispersion relation methods. In effect we are required to study a set of simultaneous dispersion relations. The problem is completely soluble and serves to clarify the essential structure of dispersion methods. The results agree with what one obtains, more easily in the present case, by direct methods
Form factors in β decay and μ capture
We suppose that β decay and μ capture are described by a universal vector and axial vector Lagrangian and we consider, via dispersion relation techniques, the properties of the corresponding S-matrix elements. Owing to the strong interactions of the nucleons, the structure of the S matrix is expected to be more complicated than that of the Lagrangian. In the former, vector and axial vector terms appear, but with coefficients which in general depend on the invariant nucleon momentum transfer; they can be thought of as Fermi interaction form factors. Moreover, two additional kinds of terms can appear in the S-matrix elements: one which simulates a direct pseudoscalar coupling and one which simulates a direct coupling involving derivatives of the nucleon wave functions. The latter is probably too small to have any experimental significance. The former, though negligible in β decay, may be appreciable in μ capture. We estimate the effective pseudoscalar coupling coefficient there to be about eight times as large as the axial vector coefficient. More generally, we investigate the structure of the various form factors; and we also reconsider, in further refinement, a recent quantitative discussion which we have given of π→μ+ν decay
Decay of the pi meson
A quantitative study of π→μ+ν decay is presented using the techniques of dispersion theory. The discussion is based on a model in which the decay occurs through pion disintegration into a nucleon-antinucleon pair, the latter annihilating via a Fermi interaction to produce the leptons. The weak vertex contains effectively both axial vector and pseudoscalar couplings even if one adopts the point of view of a universal axial vector and vector Fermi interaction. The pion-nucleon vertex which enters our model is also calculated using dispersion techniques. Under the assumption that this vertex is damped for large momentum transfers, we obtain a result for the pion lifetime largely independent of the detailed properties of the vertex and one which is in very close agreement with experiment. The precise prediction of our theory depends on the energy dependence of the complex phase shift for nucleon-antinucleon scattering in the 1S0 isotopic triplet state
Elementary Derivation of the Chiral Anomaly
An elementary derivation of the chiral gauge anomaly in all even dimensions
is given in terms of noncommutative traces of pseudo-differential operators.Comment: Minor errors and misprints corrected, a reference added. AmsTex file,
12 output pages. If you do not have preloaded AmsTex you have to \input
amstex.te
Trace anomalies and chiral Ward identities
In a simple abelian spinor field theory, the canonical trace identities for
certain axial-vector and axial-scalar operators are reexamined in dimensional
regularization, some disagreements with previous results are found and an
interesting new phenomenon is observed and briefly discussed.Comment: 4 pages, no figure, typos remove
On the induced gauge invariant mass
We derive a general expression for the gauge invariant mass (m_G) for an
Abelian gauge field, as induced by vacuum polarization, in 1+1 dimensions. From
its relation to the chiral anomaly, we show that m_G has to satisfy a certain
quantization condition. This quantization can be, on the other hand, explicitly
verified by using the exact general expression for the gauge invariant mass in
terms of the fermion propagator. This result is applied to some explicit
examples, exploring the possibility of having interesting physical situations
where the value of departs from its canonical value. We also study the
possibility of generalizing the results to the 2+1 dimensional case at finite
temperature, showing that there are indeed situations where a finite and
non-vanishing gauge invariant mass is induced.Comment: 18 pages, Latex, 3 figures (pstex
Luttinger theorem for a spin-density-wave state
We obtained the analog of the Luttinger relation for a commensurate
spin-density-wave state. We show that while the relation between the area of
the occupied states and the density of particles gets modified in a simple and
predictable way when the system becomes ordered, a perturbative consideration
of the Luttinger theorem does not work due to the presence of an anomaly
similar to the chiral anomaly in quantum electrodynamics.Comment: 4 pages, RevTeX, 1 figure embedded in the text, ps-file is also
available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.htm
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