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\(p\)-adic quantum mechanics with \(p\)-adic valued functions. (English) Zbl 0746.46067
Summary: An extension of the formalism of quantum mechanics to the case where the canonical variables and functions are valued in a field of \(p\)-adic numbers is considered. A new \(p\)-adic integral calculus is used for the realization of the Gauss representation in \(p\)-adic quantum mechanics.

MSC:
46N50 Applications of functional analysis in quantum physics
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
81S40 Path integrals in quantum mechanics
46G12 Measures and integration on abstract linear spaces
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[1] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[2] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[3] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[4] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[5] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[6] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[7] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[8] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[9] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[10] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[11] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[12] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[13] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[14] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[15] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[16] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[17] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[18] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[19] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[20] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[21] DOI: 10.1007/BF01016111 · Zbl 0698.43006
[22] DOI: 10.1007/BF00397056 · Zbl 0702.35219
[23] DOI: 10.1007/BF00397056 · Zbl 0702.35219
[24] DOI: 10.1007/BF00397056 · Zbl 0702.35219
[25] DOI: 10.1007/BF02099371 · Zbl 0239.46041
[26] DOI: 10.1007/BF02099371 · Zbl 0239.46041
[27] DOI: 10.1007/BF02099371 · Zbl 0239.46041
[28] DOI: 10.1007/BF02099371 · Zbl 0239.46041
[29] DOI: 10.1007/BF02099371 · Zbl 0239.46041
[30] DOI: 10.1007/BF02099371 · Zbl 0239.46041
[31] DOI: 10.1007/BF01018218 · Zbl 0622.35082
[32] DOI: 10.1007/BF01018218 · Zbl 0622.35082
[33] DOI: 10.1007/BF01018218 · Zbl 0622.35082
[34] DOI: 10.1007/BF01018218 · Zbl 0622.35082
[35] DOI: 10.1007/BF01018218 · Zbl 0622.35082
[36] DOI: 10.1007/BF01018218 · Zbl 0622.35082
[37] DOI: 10.1112/jlms/s2-20.1.101 · Zbl 0406.12009
[38] DOI: 10.1112/jlms/s2-20.1.101 · Zbl 0406.12009
[39] Khrennikov A. Yu., Theor. Math. Phys. 73 pp 420– (1988)
[40] DOI: 10.1070/RM1988v043n02ABEH001713 · Zbl 0665.46031
[41] Khrennikov A. Yu., Differential Equations 24 pp 2144– (1988)
[42] Khrennikov A. Yu., Diff. Eq. 25 pp 505– (1989)
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