2,125 research outputs found

    Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory

    Get PDF
    Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the SS matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.Comment: 7 page

    Flexible Graphene Transistor Architecture for Optical Sensor Technology.

    Get PDF
    Ph.D. Thesis. University of Hawaiʻi at Mānoa 2017

    The Delta-Delta Intermediate State in 1S0 Nucleon-Nucleon Scattering From Effective Field Theory

    Full text link
    We examine the role of the Delta-Delta intermediate state in low energy NN scattering using effective field theory. Theories both with and without pions are discussed. They are regulated with dimensional regularization and MSbar subtraction. We find that the leading effects of the Delta-Delta state can be absorbed by a redefinition of the contact terms in a theory with nucleons only. It does not remove the requirement of a higher dimension operator to reproduce data out to moderate momentum. The explicit decoupling of the Delta-Delta state is shown for the theory without pions.Comment: 16 pages, 3 figures, uses harvma

    Bound States and Power Counting in Effective Field Theories

    Get PDF
    The problem of bound states in effective field theories is studied. A rescaled version of nonrelativistic effective field theory is formulated which makes the velocity power counting of operators manifest. Results obtained using the rescaled theory are compared with known results from NRQCD. The same ideas are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to analyze when the Yukawa potential can be replaced by a delta-function potential. The implications of these results for the study of nucleon-nucleon scattering in chiral perturbation theory is discussed.Comment: 23 pages, eps figures, uses revte

    Complex collective states in a one-dimensional two-atom system

    Full text link
    We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance x21x_{21}. We restrict our attention to states where one atom is excited and the other is in the ground state, in symmetric or anti-symmetric combinations. We obtain exact collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, leading to long-range cooperative effects. The decay rates and the energy oscillate with the distance x21x_{21}. Depending on x21x_{21}, the decay rates will either decrease, vanish or increase as compared with the one-atom decay rate. We have sub- and super-radiance at periodic intervals. Our model may be used to study two-cavity electron wave-guides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.

    Multiphysics Modelling and Simulation in Engineering

    Get PDF

    Causality, delocalization and positivity of energy

    Full text link
    In a series of interesting papers G. C. Hegerfeldt has shown that quantum systems with positive energy initially localized in a finite region, immediately develop infinite tails. In our paper Hegerfeldt's theorem is analysed using quantum and classical wave packets. We show that Hegerfeldt's conclusion remains valid in classical physics. No violation of Einstein's causality is ever involved. Using only positive frequencies, complex wave packets are constructed which at t=0t = 0 are real and finitely localized and which, furthemore, are superpositions of two nonlocal wave packets. The nonlocality is initially cancelled by destructive interference. However this cancellation becomes incomplete at arbitrary times immediately afterwards. In agreement with relativity the two nonlocal wave packets move with the velocity of light, in opposite directions.Comment: 14 pages, 5 figure
    • 

    corecore