Introduction to the neutrix calculus

1959 ◽  
Vol 7 (1) ◽  
pp. 281-398 ◽  
Author(s):  
J. G. van der Corput
Keyword(s):  
Neutrix Calculus

scholarly journals Neutrix calculus IIc

1961 ◽  
Vol 64 ◽  
pp. 25-37
Author(s):  
J.G. van der Corput
Keyword(s):  
Neutrix Calculus

scholarly journals Neutrix calculus IIa

1961 ◽  
Vol 64 ◽  
pp. 1-14 ◽  
Author(s):  
J.G. van der Corput
Keyword(s):  
Neutrix Calculus

scholarly journals AN APPLICATION OF NEUTRIX CALCULUS TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 297-312 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Field Theories ◽  
Quantum Gravity ◽  
Asymptotic Series ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Neutrix Calculus

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories will then appear to be more manageable.

scholarly journals Neutrix calculus IIb

1961 ◽  
Vol 64 ◽  
pp. 15-24 ◽  
Author(s):  
J.G. van der Corput
Keyword(s):  
Neutrix Calculus

scholarly journals The neutrix convolution product inZ′(m)and the exchange formula

1998 ◽  
Vol 21 (4) ◽  
pp. 695-700 ◽  
Author(s):  
C. K. Li ◽  
E. L. Koh
Keyword(s):  
Fourier Transform ◽  
Quantum Theory ◽  
Dimensional Space ◽  
Distribution Theory ◽  
Convolution Product ◽  
Delta Sequence ◽  
The Fourier Transform ◽  
Neutrix Calculus ◽  
Products Of Distributions

One of the problems in distribution theory is the lack of definition for convolutions and products of distribution in general. In quantum theory and physics (see e.g. [1] and [2]), one finds that some convolutions and products such as1x⋅δare in use. In [3], a definition for product of distributions and some results of products are given using a specific delta sequenceδn(x)=Cmnmρ(n2r2)in anm-dimensional space. In this paper, we use the Fourier transform onD′(m)and the exchange formula to define convolutions of ultradistributions inZ′(m)in terms of products of distributions inD′(m). We prove a theorem which states that for arbitrary elementsf˜andg˜inZ′(m), the neutrix convolutionf˜⊗g˜exists inZ′(m)if and only if the productf∘gexists inD′(m). Some results of convolutions are obtained by employing the neutrix calculus given by van der Corput [4].

Neutrix calculus I

1960 ◽  
Vol 63 ◽  
pp. 115-123 ◽  
Author(s):  
J.G. van der Corput
Keyword(s):  
Calculus I ◽  
Neutrix Calculus
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