TY - CHAP

T1 - Nonperturbative Contribution to Φ+U

T2 - Proof of Theorem 8.2.5

AU - Bauerschmidt, Roland

AU - Brydges, David C.

AU - Slade, Gordon

N1 - Publisher Copyright:
© 2019, Springer Nature Singapore Pte Ltd.

PY - 2019

Y1 - 2019

N2 - We prove the main estimates on the nonperturbative contribution to the flow of coupling constants, i.e., to the flow of the perturbative coordinate of the renormalisation group map. This proves one of the two main theorems from the previous chapter. The proof makes use of an “extended norm” which is defined in this chapter. The main work in the proof rests on the proof of various norm estimates for polynomials in the field. A more comprehensive set of estimates on polynomials, needed for the next chapter, is also presented here.

AB - We prove the main estimates on the nonperturbative contribution to the flow of coupling constants, i.e., to the flow of the perturbative coordinate of the renormalisation group map. This proves one of the two main theorems from the previous chapter. The proof makes use of an “extended norm” which is defined in this chapter. The main work in the proof rests on the proof of various norm estimates for polynomials in the field. A more comprehensive set of estimates on polynomials, needed for the next chapter, is also presented here.

KW - Flow of coupling constants

KW - Polynomial norm estimates

KW - Renormalisation group flow

UR - http://www.scopus.com/inward/record.url?scp=85074630722&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074630722&partnerID=8YFLogxK

U2 - 10.1007/978-981-32-9593-3_9

DO - 10.1007/978-981-32-9593-3_9

M3 - Chapter

AN - SCOPUS:85074630722

T3 - Lecture Notes in Mathematics

SP - 139

EP - 149

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -