By M. J. Ray
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Additional info for Aboriginal language use in the Northern Territory: 5 reports (Work papers of SIL-AAB)
KL , p1 , . . pN )dD−z k1 · · · dD−z kL := e− P tj m2j − P tj Fj (κ(t),p)2 f (p, t) det(A(t))−(D−z)/2−n dt, with the last line obtained as we just described. The integral is convergent when the real part of z is sufficiently large. We now discuss the existence of a meromorphic continuation to the complex plane. The mathematical treatment, cf. g.  is based on the following result of Bernstein , applied to the polynomial det(A(t)). 6. Let Q(t) be a polynomial in n variables. There exists a polynomial q(D) and a polynomial differential operator L(D) in n variables, whose coefficients are polynomials in D, such that L(D) Q−D/2 = q(D) Q−D/2−1 , ∀D.
E. as the zero of its inverse p2 + m2 − Π(p2 ) = 0 for p2 = − m2phys . Let m = mphys denote the physical mass. After introducing a cutoff parameter Λ one writes m20 = m2 − δm2 (Λ). 2 In this way one views the term −δm2 (Λ) φ2 as an interaction term in the Lagrangian. Thus, one does perturbation theory with the free part given by the (Euclidean) propagator (p2 +m2 )−1 and one determines δm2 in perturbation theory as a function of a regularization parameter, such as a cutoff Λ, in such a way that it cancels the 3.
8 (x2 + y 2 + z 2 )4 The energy of the fluid disturbance is then the integral E(x, y, z) dxdydz = λρ v 2 Bc 3. FEYNMAN DIAGRAMS 41 Figure 9. Self-energy of an immersed ball in the complement B c of B. An easy direct computation shows that one has 1 1 λρ = M , λρ v 2 = M v 2 , 4 4 where M is the mass of the fluid contained in the volume of the ball B. As shown by Green , this implies that the inertial mass m that appears in Newton’s law of motion for the ball B undergoes, by the mere presence of the surrounding fluid, a “renormalization” M m0 → m = m0 + δm = m0 + .