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Natural Science Forum / Physics / Research / September 2007Feynman Propagator
Hello everyone, does anybody know if there is a general formula for the position representation for the feynman propagator of a massive scalar field in a spacetime of arbitrary dimension and signature? If yes i would be most grateful for a reference. T Hello T: I cannot answer the specific question, but I recall a relevant comment in a particle field theory book by Kaku. To find the propagator, all one needs to do is to invert the field equations. That cannot be done for a gauge theory until you choose the gauge. Weinberg wrote a few papers in the 1960's that were suppose to be an arbitrary spin approach, but I found those articles too technical to understand. All I wanted was the propagator for a massless spin 2 field (if anyone knows it, feel free to send it to me off the group at sweetser at alum mit edu). doug sweetser@alum.mit.edu schrieb: > Hello T: > [quoted text clipped - 6 lines] > arbitrary spin approach, but I found those articles too technical to > understand. Weinberg's papers on 'Feynman rules for any spin' and some related questions are Phys.Rev. 133 (1964), B1318-B1322 any spin (massive) Phys.Rev. 134 (1964), B882-B896 any spin II (massless) Phys.Rev. 135 (1964), B1049-B1056 grav. mass = inertial mass Phys.Rev. 138 (1965), B988-B1002 derivation of Einstein Phys.Rev. 140 (1965), B516-B524 infrared gravitons Phys.Rev. 181 (1969), 1893-1899 any spin III (general reps.) A perhaps more understandable version of part of the material is in D.N. Williams, The Dirac Algebra for Any Spin, Unpublished Manuscript (2003) http://www-personal.umich.edu/~williams/papers/diracalgebra.pdf http://ptp.ipap.jp/link?PTP/51/249/ constructs covariant propagators and complete vertices for spin J bosons with conserved currents for all J. Arnold Neumaier > sweetser@alum.mit.edu schrieb: > > Hello T: [quoted text clipped - 25 lines] > constructs covariant propagators and complete vertices for spin J bosons > with conserved currents for all J. Phys.Rev. 135 (1964), B1049-B1056 grav. mass = inertial mass http://prola.aps.org/abstract/PR/v135/i4B/pB1049_1 Lorentz invariance is assumed Affine and teleparallel gravitation theories wholly contain GR. They disjointly additionally allow for an anisotropic chiral vacuum background that violates Lorentz invariance. Chemically identical maximally opposite parity mass distributions would 1) violate the Equivalence Principle. They would locally vacuum free fall along divergent (diastereotopic) minimum action trajectories (left or right shoes on a vacuum left foot); 2) violate conservation of angular momentum. Noether's theorem requires isotropic vacuum for coupling symmetry to conserved observable. 3) evince measurable divergences. Any substance grown as single crystals in enantiomorphic space groups P3(1)21 and P3(2)21 (the quartz group) qualifies. Benzil (Ph-CO-CO-Ph, mp=95 C) allows a rapid, simple, remarkably sensitive parity calorimetry experiment performed in off-the-shelf hardware. It allows separation of parity-divergent chiral vacuum insertion energies (time-independent) and Equivalence Principle parity violation (dependent upon time of day and geographic orientation of the test masses, as with an Eotvos experiment). It is quantitative. A non-null output allows prediction of the corresponding parity Eotvos experiment non-zero net output performed with alpha-quartz. http://www.mazepath.com/uncleal/lajos.htm#a2 scheduled for Christmas 2007  SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 You find this and a whole bunch of other functions nicely discussed in Pauli Lectures on Physics, Vol. 6, Selected Topics in Field Quantization, Dover Publications a masterpiece textbook series (especially the volume on non-relativistich quantum mechanics!), although a bit oldfashioned (especially this volume 6), but one clearly sees the didactic heritage of Pauli's great teacher, Arnold Sommerfeld, whose lecture notes are the best source for classical physics. It's a textbook style which sadly seems to be lost nowadays! > Hello everyone, > [quoted text clipped - 4 lines] > > T SignatureHendrik van Hees Texas A&M University Phone: +1 979/845-1411 Cyclotron Institute, MS-3366 Fax: +1 979/845-1899 College Station, TX 77843-3366 http://theory.gsi.de/~vanhees/faq mailto:hees@comp.tamu.edu Thank you all for the references but it seems most of you have misunderstood what i asked for. It wasn't the feynman propagator for arbitrary spin, rather the *position representation* of the feynman propagator of the usual massive scalar field (spin 0) in a spacetime of *arbitrary dimension* whose metric has *arbitrary signature* (so for example the answer would be some function of the spacetime interval that depends on the dimension of the spacetime D and on the type of the metric put on it, for example D=8, and signature ++++ +---). Note that essentially the answer amounts to taking the Fourier transform of the simple function 1/(p^2 - m^2 + i epsilon) with respect to p (p is of course a D-dimensional vector and p^2 is defined of course with the given metric). I expect it to be some sort of a bessel function as this is the answer for the 4d and 3d cases in the riemannian and lorentzian metric signatures. Dear Hendrik, does this book has the explicit formulae relevant? Regards, T > You find this and a whole bunch of other functions nicely discussed in > [quoted text clipped - 9 lines] > > T.M.T...@gmail.com wrote: > > Hello everyone, > [quoted text clipped - 9 lines] > Phone: +1 979/845-1411 Cyclotron Institute, MS-3366 > Fax: +1 979/845-1899 College Station, TX 77843-3366http://theory.gsi.de/~vanhees/faq mailto:h...@comp.tamu.edu > Dear Hendrik, does this book has the explicit formulae relevant? Yes, but only for the physical case of d=4. SignatureHendrik van Hees Texas A&M University Phone: +1 979/845-1411 Cyclotron Institute, MS-3366 Fax: +1 979/845-1899 College Station, TX 77843-3366 http://theory.gsi.de/~vanhees/faq mailto:hees@comp.tamu.edu |
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