Summary
Two new second order space-time correlation tensors
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and
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are introduced, which are simple linear combinations of the correlation tensors discussed in Part I of this investigation (x 1,x 2 are position vectors of two points andτ a time delay). These new tensors are intimately related to certain generalizations of the (time averaged) energy density and the energy flow vector. Differential equations which
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2FBF02860406/MediaObjects/40762_2008_Article_BF02860406_f3.jpg)
and
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2FBF02860406/MediaObjects/40762_2008_Article_BF02860406_f4.jpg)
satisfy in free space are derived, and from them four new conservation laws are deduced. In the limitx 1→x 2,τ→0 two of these laws reduce to the usual laws (in time averaged form) for the conservation of the energy and the momentum in an electromagnetic field. The other two laws reduce only to trivial identities in this limit, so that they have no analogy in the framework of the usual theory.
Riassunto
Si introducono due nuovi tensori del secondo ordine di correlazione dello spazio tempo
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2FBF02860406/MediaObjects/40762_2008_Article_BF02860406_f5.jpg)
eH ik (x 1,x 2,τ), che sono semplici combinazioni lineari dei tensori di correlazione discussi nella Parte I di questo studio (x 1,x 2 sono i vettori di posizione di due punti eτ un ritardo nel tempo). Questi nuovi tensori sono intimamente connessi a certe generalizzazioni della densità di energia (mediata rispetto al tempo) e del vettore del flusso di energia. Si derivano le equazioni differenziali, che sono soddisfatte da
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2FBF02860406/MediaObjects/40762_2008_Article_BF02860406_f6.jpg)
eH jk nello spazio libero, e da esse vengono dedotte quattro nuove leggi di conservazione. Al limite perx 1→x 2,τ→0, due di queste leggi si riducono alle leggi usuali (in forma mediata rispetto al tempo) per la conservazione dell’energia e della quantità di moto in un campo elettromagnetico. Le altre due leggi, a tale limite, si riducono semplicemente ad identità banali, cosichè esse non hanno alcun analogo nella schema della teoria usuale.
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References
P. Roman andE. Wolf:Nuovo Cimento,17, 461 (1960).
M. Born andE. Wolf:Principles of Optics (London and New York, 1959), chap. X.
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This research was supported in part by the United States Air Force under Contract no. AF 49(638)-602, monitored by the AF Office of Scientific Research of the Air Research and Development Command.
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Roman, P., Wolf, E. Correlation theory of stationary electromagnetic fields. Nuovo Cim 17, 477–490 (1960). https://doi.org/10.1007/BF02860406
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DOI: https://doi.org/10.1007/BF02860406