Search results for "Mathematical physics"
showing 10 items of 2687 documents
Spherical random-field systems with long-range interactions: general results and application to the Coulomb glass
1993
A classical spherical random-field Hamiltonian with long-range (power-law) interactions is investigated by means of the replica theory. Both ferromagnetic and anti-ferromagnetic interactions are considered. The use of continuous variables instead of Ising variables in the spherical version of the model allows one to calculate the free energy exactly. The existence of an equilibrium phase transition is investigated based on the replica-symmetric solution. The results are applied to the Coulomb-glass model of interacting localized electrons in a disordered solid. This model is shown not to have an equilibrium phase transition for spatial dimensions D 4 the model has a phase transition to an o…
Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
2015
We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.
Infra-Red Asymptotic Dynamics of Gauge Invariant Charged Fields: QED versus QCD
1999
The freedom one has in constructing locally gauge invariant charged fields in gauge theories is analyzed in full detail and exploited to construct, in QED, an electron field whose two-point function W(p), up to the fourth order in the coupling constant, is normalized with on-shell normalization conditions and is, nonetheless, infra-red finite; as a consequence the radiative corrections vanish on the mass shell $p^2=\mu^2$ and the free field singularity is dominant, although, in contrast to quantum field theories with mass gap, the eigenvalue $\mu^2$ of the mass operator is not isolated. The same construction, carried out for the quark in QCD, is not sufficient for cancellation of infra-red …
Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
2004
We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)-improved Wilson action. The results are obtained in the quenched approximation at four values of the lattice coupling by using the non-perturbative RI/MOM renormalization method. Several sources of systematic uncertainties, including discretization errors and final volume effects, are examined. The contribution of the Goldstone pole, which in some cases may affect the extrapolation of the renormalization constants to the chiral limit, is non-perturbatively subtracted. The scale independent renormalization constants of bilinear quark…
Minimally doubled fermions at one loop
2009
Minimally doubled fermions have been proposed as a cost-effective realization of chiral symmetry at non-zero lattice spacing. Using lattice perturbation theory at one loop, we study their renormalization properties. Specifically, we investigate the consequences of the breaking of hyper-cubic symmetry, which is a typical feature of this class of fermionic discretizations. Our results for the quark self-energy indicate that the four-momentum undergoes a renormalization which contains a linearly divergent piece. We also compute renormalization factors for quark bilinears, construct the conserved vector and axial-vector currents and verify that at one loop the renormalization factors of the lat…
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
2007
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of $\Delta{B}=2$ parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by non-perturbatively ${\rm O}(a)$ improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in …
Quark mass dependence of the one-loop three-gluon vertex in arbitrary dimension
2001
The one-loop off-shell massive quark contribution to the three-gluon vertex is calculated in an arbitrary space-time dimension. The results for all relevant on-shell and symmetric limits are obtained directly from the general off-shell results. The analytic structure of the results for the relevant massive scalar integrals is also discussed.
Next-to-leading order renormalization of the $\Delta B=2$ operators in the static theory
1996
The renormalization, at the next-to-leading order in $\alpha_s$, of the $\Delta B=2$ operators at the lowest order in the heavy quark expansion, namely in the static theory, is computed taking into account previously missed contributions. These operators are relevant for the calculation of the $B^0$--$\bar B^0$ mixing on the lattice.
ΔF=2 effective Lagrangian in theories with vector-like fermions
1997
In this work we analyze a new piece present in the $\Delta F = 2$ effective Lagrangian in models with extra vector-like quarks. This piece, which was not taken into account previously, is required in order to preserve gauge invariance once the unitarity of the CKM matrix is lost. We illustrate the effects of this new piece in both, CP conserving and CP violating processes.
The CP-Conserving Direction
1998
A symmetry transformation is well defined in the case of an invariant theory, being the corresponding operator undetermined otherwise. However, we show that, even with CP violation, it is possible to determine the CP transformation by separating the Lagrangian of the Standard Model in a CP-conserving and a CP-violating part, in a unique way, making use of the empirically known quark mixing hierarchy. To order \lambda^3 for the Bd-system, the CP-conserving direction matches one of the sides of the (bd) unitarity triangle. We use this determination to calculate the rephasing invariant parameter \epsilon, which measures CP-mixing in the B0-B0bar system.