We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization reproduces the quantum critical behavior expected from the Hertz-Millis analysis, and verify that this theory has dynamic critical exponent z = 3. Going beyond this framework, we study the behavior of the fermion degrees of freedom directly, and show that at quantum criticality as well as in the the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasi-particles of the normal Fermi liquid are generally wiped out. Instead, they exhibit short ranged spatial correlations that decay faster than any power-law, with the law |x| −1 exp(−const. |x| 1/3 ) and we verify explicitely the vanishing of the fermion residue utilizing this expression. In contrast, the fermion auto-correlation function has the behavior |t| −1 exp(−const. |t| −2/3 ). In this regime we also find that, at low frequency, the single-particle fermion density-of-states behaves as N * (ω) = N * (0) + B ω 2/3 log ω + . . ., where N * (0) is larger than the free Fermi value, N (0), and B is a constant. These results confirm the non-Fermi liquid nature of both the quantum critical theory and of the nematic phase.

A recently proposed path-integral bosonization scheme for massive fermions in 3 dimensions is extended by keeping the full momentum-dependence of the one-loop vacuum polarization tensor. This makes it possible to discuss both the massive and massless fermion cases on an equal footing, and moreover the results it yields for massless fermions are consistent with the ones of another, seemingly different, canonical quantization approach to the problem of bosonization for a massless fermionic field in 3 dimensions.

We argue that in the infrared regime of continuum Yang-Mills theory, the possibility of a mass gap in the charged sector is closely associated with the center vortex sector. The analysis of the possible consequences of the ensembles of defects is done by showing that the description of center vortices and monopoles is naturally unified by means of a careful treatment of Cho decomposition. If on the one hand confinement is usually associated with monopole condensation in a compact abelian model, in this scenario, the previous decoupling of the offdiagonal degrees of freedom, for the abelian model dominate at large distances, can be understood as induced by a phase where center vortices become thick objects. Other important scenarios for correlated monopoles and center vortices, observed in lattice simulations, are also accomodated in our general formulation.

We consistently quantize a class of relativistic non-local field equations characterized by a non-local kinetic term in the lagrangian. We solve the classical non-local equations of motion for a scalar field and evaluate the on-shell hamiltonian. The quantization is realized by imposing Heisenberg's equation which leads to the commutator algebra obeyed by the Fourier components of the field. We show that the field operator carries, in general, a reducible representation of the Poincare group.We also consider the Gupta-Bleuler quantization of a non-local gauge field and analyze the propagators and the physical states of the theory.

We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly calculated in terms of the concurrence. As a main result, we predict a fractional topological phase for cyclic evolutions in the multiply connected space of maximally entangled states.PACS numbers: PACS: 03.65. Vf, 03.67.Mn, 07.60.Ly, 42.50.Dv In a seminal work, M. Berry [1] showed the important role played by geometric phases in quantum theory. Since then, the interest for geometric phases was renewed by potential applications to quantum computation. The experimental demonstration of a conditional phase gate was provided both in Nuclear Magnetic Resonance (NMR) [2] and trapped ions [3]. Optical geometric phases have already been discussed both for polarization [4] and vortex mode transformations [5,6]. The role of entanglement in the phase evolution of qubits was investigated in refs. [7,8]. Recently, P. Milman and R. Mosseri [9,10] investigated the geometric phase and the topological structure associated with cyclic evolutions of arbitrary two-qubit pure states. This structure has been experimentally evidenced in the context of spin-orbit mode transformations of a laser beam [11] and in NMR [12]. Although the topological nature of the phase acquired by maximally entangled states is well settled, the distinction between geometrical and topological phases has not been established clearly for partially entangled states. In this work we present a group theoretical approach which allows for a clear distinction between the two aspects. As a bonus, this approach is easily extended to higher dimensions, bringing an interesting prediction of a fractional topological phase.Let |ψ = d i,j=1 α ij |ij be the most general twoqudit pure state. We shall represent this state by the d × d matrix α whose elements are the coefficients α ij . With this notation the norm of the state vector becomes ψ|ψ = T r(α † α) = 1 and the scalar product between two states is φ|ψ = T r(β † α), where β is the d × d matrix containing the coefficients of state |φ in the chosen basis. We are interested in the phase evolution of the state |ψ under local unitary operations. So let us take two unitary matrices U A and U B belonging to U (d) and representing the operations performed in each subsystem separately. Under these unitary operations the state matrix will evolve as α(t) = U A α(0) U ⊺ B , where U j (t) = e iφj (t)Ū j (t) (j = A, B) andŪ j ∈ SU (d). One can identify the following invariants under local unitary evolutions: T r[ρ aim, we will analyze the topology of the space of two-qudit states and how the total phase is built. In this regard, we would like to underline that according to ref. [14], the geometric phase acquired by a time evolving quantum state α(t) is always defined asthat corresponds to the total phase minus the dynamical phase. Therefore, a topological phase, that is, an object that only dep...

General results on the structure of the bosonization of fermionic systems in (2 + 1)d are obtained. In particular, the universal character of the bosonized topological current is established and applied to generic fermionic current interactions. The final form of the bosonized action is shown to be given by the sum of two terms. The first one corresponds to the bosonization of the free fermionic action and turns out to be cast in the form of a pure Chern-Simons term, up to a suitable nonlinear field redefinition. We show that the second term, following from the bosonization of the interactions, can be obtained by simply replacing the fermionic current by the corresponding bosonized expression.2

Using the bosonization approach, we study fermionic systems with a nonlinear dispersion relation in dimension dу2. We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi-liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent-state path-integral technique, we built up the effective action that governs the dynamics of the Fermi-surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters ͑Pomeranchuck instabilities͒. In particular, we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.

In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path-integral displays a BRST symmetry, however, it cannot be globally extended due to sector dependent boundary conditions on the ghost fields. These are nice features as they would permit to discuss the independence of the partial contributions on gauge parameters,, while opening a window for the space of quantum states to be different from the perturbative one, which would be implied if topological configurations were removed.