The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional regularization. In the renormalized version of the theory, there is a strong-coupling regime where quantum-mechanical breaking of scale symmetry takes place through dimensional transmutation, with the creation of a single bound state and of an energydependent s-wave scattering matrix element.PACS numbers: 03.65. Ge, 03.65.Nk, 11.10.Gh, The quantum-mechanical inverse square potential is a singular problem that has generated controversy for decades. For instance, the solution proposed in Ref.[1] failed to give a Hamiltonian bounded from below, and this led to a number of alternative regularization techniques [2-4] based on appropriate parametrizations of the potentialincluding the replacement [5] of self-adjointness by an interpretation of the "fall of the particle to the center" [6]. However, it is generally recognized that the singular nature of this problem lies in that its Hamiltonian, being symmetric but not self-adjoint, admits self-adjoint extensions [7]. Recently, a renormalized solution was presented using field-theoretic techniques [8], but it was just limited to the one-dimensional case and cutoff renormalization.In this Letter (i) we generalize the results of Ref.[8] to D dimensions (including the all-important D = 3 case) using cutoff regularization in configuration space; (ii) present a complete picture of the renormalized theory; and (iii) confirm the same conclusions using dimensional regularization [9]. This problem is crucial for the analysis and interpretation of the point dipole interaction of molecular physics [10,11], and may be relevant in polymer physics [12]. In addition (i) it displays remarkable similarities with the two-dimensional δ-function potential [13][14][15]; (ii) it provides another example of dimensional transmutation [16] in a system with a finite number of degrees of freedom; and (iii) it illustrates the relevance of field-theoretic concepts in quantum mechanics [13][14][15]17].This problem is ideally suited for implementation in configuration space [18], where the radial Schrödinger equation for a particle subject to the r −2 potential in D dimensions [19] reads (withh = 1 and 2m = 1)which is explicitly scale-invariant because λ is dimensionless [20]. In Eq. (1), l is the angular momentum quantum number and λ > 0 corresponds to an attractive potential; with the transformation R l (r) = r −(D−1)/2 u l (r), Eq. (1) If λ were allowed to vary, one would see that the nature of the solutions changes around the critical value λ ( * ) l , for each angular momentum state. For λ < λ ( * ) l (including repulsive potentials), the order s l of the Bessel functions is real, so that the solution regular at the origin is proportional to the Bessel function of the first kind J s l √ E r . However, the same solution fails to satisfy the required behavior at ...

The interaction of an electron with a polar molecule is shown to be the simplest realization of a quantum anomaly in a physical system. The existence of a critical dipole moment for electron capture and formation of anions, which has been confirmed experimentally and numerically, is derived. This phenomenon is a manifestation of the anomaly associated with quantum symmetry breaking of the classical scale invariance exhibited by the point-dipole interaction. Finally, analysis of symmetry breaking for this system is implemented within two different models: point dipole subject to an anomaly and finite dipole subject to explicit symmetry breaking.

Magnetic monopoles have been a subject of interest since Dirac established the relation between the existence of monopoles and charge quantization. The intense experimental search carried thus far has not met with success. The Large Hadron Collider is reaching energies never achieved before allowing the search for exotic particles in the TeV mass range. In a continuing effort to discover these rare particles we propose here other ways to detect them. We study the observability of monopoles and monopolium, a monopole-antimonopole bound state, at the Large Hadron Collider in the γ γ channel for monopole masses in the range 500-1000 GeV. We conclude that LHC is an ideal machine to discover monopoles with masses below 1 TeV at present running energies and with 5 fb −1 of integrated luminosity. Pacs: 14.80.Hv, 95.30.Cq,

We analyze spin dependent parton distributions consistent with the most recent measurements of the spin dependent deep inelastic scattering structure functions and obtained in the framework of the spin dilution model. Predictions for the doubly polarised proton-proton Drell-Yan asymmetry, for the high p T photon production mechanism and J/Ψ excitation are calculated using these distributions and are shown to be particularly adequate to unveil the polarisation of partons in the proton.