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C. D. Fosco

Publications and source records attributed to C. D. Fosco.

At least 91 records · Page 5Linked to original sources
arXiv2005

Planar field theories with space-dependent noncommutativity

We study planar noncommutative theories such that the spatial coordinates ${\hat x}_1$, ${\hat x}_2$ verify a commutation relation of the form: $[{\hat x}_1, {\hat x}_2] = i θ({\hat x}_1,{\hat x}_2)$. Starting from the operatorial representation for dynamical variables in the algebra generated by ${\hat x}_1$ and ${\hat x}_2$, we introduce a noncommutative product of functions corresponding to a specific operator-ordering prescription. We define derivatives and traces, and use them to construct scalar-field actions. The resulting expressions allow one to consider situations where an expansion in powers of $θ$ and its derivatives is not necessarily valid. In particular, we study in detail the case when $θ$ vanishes along a linear region. We show that, in that case, a scalar field action generates a boundary term, localized around the line where $θ$ vanishes.

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arXiv2005

Noncommutative theories and general coordinate transformations

We study the class of noncommutative theories in $d$ dimensions whose spatial coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative theory, which satisfy the relation $[y_i, y_j] = i θ_{ij}$, with a constant $θ_{ij}$ tensor. The $x_i$ variables verify a commutation relation which is, in general, space-dependent. We study the main properties of this special kind of noncommutative theory and show explicitly that, in two dimensions, any theory with a space-dependent commutation relation can be mapped to another where that $θ_{ij}$ is constant.

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arXiv2005

Vacuum polarization in $d+{1/2}$ dimensions

We study the main properties of the one-loop vacuum polarization function ($Π_{αβ}$) for spinor $QED$ in `$d + {1/2}$ dimensions', i.e., with fields defined on ${\mathcal M} \subset {\mathbb R}^{d+1}$ such that ${\mathcal M} = \{(x_0,...,x_d) | x_{d}\geq 0 \}$, with bag-like boundary conditions on the boundary $\partial{\mathcal M} = \{(x_0,...,x_d) | x_{d}= 0 \}$. We obtain an exact expression for the induced current due to an external constant electric field normal to the boundary. We show that, for the particular case of 2+1 dimensions, there is a transverse component for the induced current, which is localized on a region close to $\partial{\mathcal M}$. This current is a parity breaking effect purely due to the boundary.

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arXiv2004

On Coordinate Transformations in Planar Noncommutative Theories

We consider planar noncommutative theories such that the coordinates verify a space-dependent commutation relation. We show that, in some special cases, new coordinates may be introduced that have a constant commutator, and as a consequence the construction of Field Theory models may be carried out by an application of the standard Moyal approach in terms of the new coordinates. We apply these ideas to the concrete example of a noncommutative plane with a curved interface. We also show how to extend this method to more general situations.

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arXiv2004

Chiral zero modes in non local domain walls

We study a generalization of the Callan-Harvey mechanism to the case of a non local mass. Using a 2+1 model as a concrete example, we show that both the existence and properties of localized zero modes can also be consistently studied when the mass is non local. After dealing with some general properties of the resulting integral equations, we show how non local masses naturally arise when radiative corrections are included. We do that for a 2+1 dimensional example, and also evaluate the zero mode of the resulting non local Dirac operator.

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arXiv2004

Chirality and parity in a first-quantized representation

We study the realization of chiral and parity transformations within a particle-like path-integral representation for Dirac fields, showing how those transformations can be implemented in a natural way within the formalism. We then obtain a representation for the chiral fermion propagator and determinant within this framework, and also formulate a way to define the average of the propagator over a random mass in $d=2n$ dimensions.

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arXiv2003

Fermion propagator for QED_3 in the IR domain

We evaluate the fermion propagator in parity-conserving QED_3 with N flavours, in the context of an IR domain approximation. This provides results which are non-perturbative in the loopwise expansion sense. We include fermion-loop effects, and show that they are relevant to the chiral symmetry breaking phenomenon, that can be understood in this context.

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arXiv2003

A gauge invariant formulation for the SU(N) non-linear sigma model in 2+1 dimensions

We derive a local, gauge invariant action for the SU(N) non-linear sigma-model in 2+1 dimensions. In this setting, the model is defined in terms of a self-interacting pseudo vector-field θ_μ, with values in the Lie algebra of the group SU(N). Thanks to a non-trivially realized gauge invariance, the model has the correct number of degrees of freedom: only one polarization of θ_μ, like in the case of the familiar Yang-Mills theory in 2+1 dimensions. Moreover, since θ_μis a pseudo-vector, the physical content corresponds to one massless pseudo-scalar field in the Lie algebra of SU(N), as in the standard representation of the model. We show that the dynamics of the physical polarization corresponds to that of the SU(N) non-linear sigma model in the standard representation, and also construct the corresponding BRST invariant gauge-fixed action.

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arXiv2002

A note on anomalous Jacobians in 2+1 dimensions

There exist local infinitesimal redefinitions of the fermionic fields, which may be used to modify the strength of the coupling for the interaction term in massless QED3. Under those (formally unitary) transformations, the functional integration measure changes by an anomalous Jacobian, which (after regularization) yields a term with the same structure as the quadratic parity-conserving term in the effective action. Besides, the Dirac operator is affected by the introduction of new terms, apart from the modification in the minimal coupling term. We show that the result coming from the Jacobian, plus the effect of those new terms, add up to reproduce the exact quadratic term in the effective action. Finally, we also write down the form a finite decoupling transformation would have, and comment on the unlikelihood of that transformation to yield a helpful answer to the non-perturbative evaluation of the fermionic determinant.

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arXiv2002

Finite temperature regularization

We present a non-perturbative regularization scheme for Quantum Field Theories which amounts to an embedding of the originally unregularized theory into a spacetime with an extra compactified dimensions of length L ~ Lambda^{-1} (with Lambda an ultraviolet cutoff), plus a doubling in the number of fields, which satisfy different periodicity conditions and have opposite Grassmann parity. The resulting regularized action may be interpreted, for the fermionic case, as corresponding to a finite-temperature theory with a supersymmetry, which is broken because of the boundary conditions. We test our proposal in a perturbative calculation (the vacuum polarization graph for a D-dimensional fermionic theory) and in a non-perturbative one (the chiral anomaly).

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arXiv2002

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 $m_G$ 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.

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arXiv2002

Quantum stability of defects for a Dirac field coupled to a scalar field in 2+1 dimensions

We study the Euclidean effective action and the full fermion propagator for a Dirac field in the presence of a scalar field with a domain wall defect, in 2+1 dimensions. We include quantum effects due to both fermion and scalar field fluctuations, in a one-loop approximation. The results are interpreted in terms of the quantum stability of the zero mode solution. We also study, for this system, the induced `inertial' electric field for the fermions on the defect, due to the quantum fluctuations of the scalar field.

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arXiv2001

Induced commutative Chern-Simons term from noncommutativity in planar systems

We test the consistency of the use of a noncommutative theory description for charged particles in a strong magnetic field, by deriving the induced Chern-Simons (CS) term for an external Abelian gauge field in 2+1 dimensions. In this description, the system is modeled by a noncommutative matter field coupled to a U(1) noncommutative gauge field, related to the original, commutative one, by a Seiberg-Witten transformation. We show that an Abelian CS term for the commutative gauge field is indeed induced, and moreover that it matches the result of previous commutative field theory calculations.

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arXiv2001

Generalized parity transformations in lattice Chern-Simons theory

Regularization modifies the (odd) behaviour of the Abelian Chern-Simons action under parity. This effect happens for any sensible regularization; in particular, on the lattice. However, as in the chiral symmetry case, there exist generalized parity transformations such that the regularized theory is odd, and the corresponding operator verifies a Ginsparg-Wilson like relation. We present a derivation of such a relation and of the corresponding symmetry transformations.

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arXiv2001

Fermionic determinant with a linear domain wall in 2+1 dimensions

We consider a Dirac field in 2+1 Euclidean dimensions, in the presence of a linear domain wall defect in its mass, and a constant electromagnetic field. We evaluate the exact fermionic determinant for the situation where the defect is assumed to be rectilinear, static, and the gauge field is minimally coupled to the fermions. We discuss the dependence of the result on the (unique) independent geometrical parameter of this system, namely, the relative orientation of the wall and the direction of the external field. We apply the result for the determinant to the evaluation of the vacuum energy.

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arXiv2001

Aspects of noncommutative descriptions of planar systems in high magnetic fields

We study some aspects of recent proposals to use the noncommutative Chern-Simons theory as an effective description of some planar condensed matter models in strong magnetic fields, such as the Quantum Hall Effect. We present an alternative justification for such a description, which may be extended to other planar systems where a uniform magnetic field is present.

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arXiv2001

Generalized parity transformations in the regularized Chern-Simons theory

We study renormalization effects in the Abelian Chern-Simons (CS) action. These effects can be non-trivial when the gauge field is coupled to dynamical matter, since the regularization of the UV divergences in the model forces the introduction of a parity even piece in the gauge field action. This changes the classical (odd) transformation properties of the pure CS action. This effect, already discussed for the case of a lattice regularization by F. Berruto, M.C. Diamantini and P. Sodano in hep-th/0004203, is also present when the theory is defined in the continuum and, indeed, it is a manifestation of a more general `anomalous' effect, since it happens for every regularization scheme. We explore the physical consequences of this anomaly. We also show that generalized, nonlocal parity transformations can be defined in such a way that the regularized theory is odd, and that those transformations tend to the usual ones when the cutoff is removed. These generalized transformations play a role that is tantamount to the deformed symmetry corresponding to Ginsparg-Wilson fermions [2] (in an even number of spacetime dimensions).

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