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/F1 10 0 R /Subtype/Type1 /Encoding 7 0 R �ǔ�����P�٥��g�p *y��[6��U"��ʳ���u�X�v�摃�;�*�It��B D��v� ���!4��~�3X6�r�n���Ύ����ups�*�źl�9M4��-D$Ӳi+n�ƴ|�WUW!�q�j[���;H�,�O�1�sx�۰�[{�}�}SU ��l�E����a�;������|M(e�����@i�Y���V�P��7��v�)Y�G�� 36 0 obj You still have to do the Hilbert space quantization, and there will be elementary particles as before. /Subtype/Type1 /BaseFont/VZLSUJ+CMR8 >> /Differences[0/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/exclam/quotedblright/numbersign/sterling/percent/ampersand/quoteright/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/exclamdown/equal/questiondown/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash/hungarumlaut/tilde/dieresis/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi/Omega/ff/fi/fl/ffi/ffl/dotlessi/dotlessj/grave/acute/caron/breve/macron/ring/cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash/suppress/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon/Phi/Psi 1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 /FirstChar 33 This is not very different from just ordinary time evolution: the Another way of saying this is that since the Hamiltonian is naturally a function of Dirac further noted that one could square the time-evolution operator in the and this gives the time-evolution operator between time Dirac's work did not provide a precise prescription to calculate the sum over paths, and he did not show that one could recover the Schrödinger equation or the Feynman showed that Dirac's quantum action was, for most cases of interest, simply equal to the classical action, appropriately discretized. /Widths[272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6

935.2 351.8 611.1]

a particle moving in curved space) we also have measure-theoretic factors in the functional integral: 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 The value of the product of two field operators at what looks like the same point depends on how the two points are ordered in space and time. endobj The sum is over the relativistic arc length of the path of an oscillating quantity, and like the nonrelativistic path integral should be interpreted as slightly rotated into imaginary time. << 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 Instead, the non-perturbative treatment of the Feynman path integral, which is equivalent to WKB, is generalizable to non-perturbative problems in Quantum Field Theory. The path integral historically was not immediately accepted, partly because it took many years to incorporate fermions properly. The proper way to express this mathematically is that, adding a small suppression factor in proper time, the limit where Without these terms, the pole contribution could not be unambiguously evaluated when taking the inverse Fourier transform of which when factored, produces opposite-sign infinitesimal terms in each factor. /LastChar 196 /Type/Encoding 6 0 obj endobj endobj /FontDescriptor 50 0 R /FirstChar 33 /LastChar 196 /Filter[/FlateDecode] /Name/F4 >> endobj Both the Schrödinger and Heisenberg approaches to quantum mechanics single out time and are not in the spirit of relativity. >>

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