Khalatnikov JETP isnt scanned yet so Khalatnikovs contribution which seem to be closer to Candlin than Salam and Matthews Feynman also does something similar to Salam and Matthews in one of the electrodynamics papers but without the Fermionic coherent states and without the justification in terms of sum over intermediate states which are both found in Candlin for the first time I think This paper talks about the result the integral over Fermionic fields is defined following Schwinger so that the action principle will work and the result is that the determinant is in the numerator and not the denominator This is most of Grassman integration but without the formal anticommuting variables which seem to have been introduced by Berezin and Candlin independently at least according to this source I did not read the original Berezin articles only the 1965 textbook so perhaps they are more complete than I originally thought If anyone has read these please include a summary of the contents The real question in my mind is as follows Feynmans propagator approach only requires that the statistics be correct when permuting the ends of the paths The rest can be done by summing over particle paths with appropriate projections to deal with Dirac eqn So the early authors between 19481954 are all dealing with formal anticommuting variables no complete theory This is true of the Schwinger action principle and to a lesser extent of Matthews and Salam Matthews and Salam like Feynman in his QEDIII paper treat the sum over histories as greens function manipulations without trying to formally define a calculus of anticommuting fields They do define anticommuting sources and anticommuting field Greens functions but this is similar to Feynman and Schwinger It does not have the crucial addition that the algebra of the fields in spacetime makes sense and the Fermi field integral is a sum over intermediate states Khalatnikov seems to have understood the modern thing that the Fermionic integral is a concept that is well defined Unfortunately I cannot access his paper If anyone has access please find out what is in there Candlin defines the whole thing in a very modern way This paper is the best on the subject I have read but it is similar to Berezin 1964 Berezin has some papers in the 1950s and 1960s which seem to develop the whole thing indepedently starting with Khalatnikovs observation These papers are also crucial who develops the Fermionic coherent states And who shows that the Fermionic integral reproduces the sum over intermediate Fermionic statesThe whole thing is somewhat implicit in Matthews and Salam but also in Schwinger and Feynman The real important development is the identification of sumoverintermediate states with grassmann integral If someone can point out who did what it would help a lot

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Khalatnikov JETP isnt scanned yet so Khalatnikovs contribution which seem to be closer to Candlin than Salam and Matthews Feynman also does something similar to Salam and Matthews in one of the electrodynamics papers but without the Fermionic coherent states and without the justification in terms of sum over intermediate states which are both found in Candlin for the first time I think This paper talks about the result the integral over Fermionic fields is defined following Schwinger so that the action principle will work and the result is that the determinant is in the numerator and not the denominator This is most of Grassman integration but without the formal anticommuting variables which seem to have been introduced by Berezin and Candlin independently at least according to this source I did not read the original Berezin articles only the 1965 textbook so perhaps they are more complete than I originally thought If anyone has read these please include a summary of the contents The real question in my mind is as follows Feynmans propagator approach only requires that the statistics be correct when permuting the ends of the paths The rest can be done by summing over particle paths with appropriate projections to deal with Dirac eqn So the early authors between 19481954 are all dealing with formal anticommuting variables no complete theory This is true of the Schwinger action principle and to a lesser extent of Matthews and Salam Matthews and Salam like Feynman in his QEDIII paper treat the sum over histories as greens function manipulations without trying to formally define a calculus of anticommuting fields They do define anticommuting sources and anticommuting field Greens functions but this is similar to Feynman and Schwinger It does not have the crucial addition that the algebra of the fields in spacetime makes sense and the Fermi field integral is a sum over intermediate states Khalatnikov seems to have understood the modern thing that the Fermionic integral is a concept that is well defined Unfortunately I cannot access his paper If anyone has access please find out what is in there Candlin defines the whole thing in a very modern way This paper is the best on the subject I have read but it is similar to Berezin 1964 Berezin has some papers in the 1950s and 1960s which seem to develop the whole thing indepedently starting with Khalatnikovs observation These papers are also crucial who develops the Fermionic coherent states And who shows that the Fermionic integral reproduces the sum over intermediate Fermionic statesThe whole thing is somewhat implicit in Matthews and Salam but also in Schwinger and Feynman The real important development is the identification of sumoverintermediate states with grassmann integral If someone can point out who did what it would help a lot

