Nonexistence of solutions of the \(p\)-adic strings. (English. Russian original) Zbl 1280.81113
Theor. Math. Phys. 174, No. 2, 178-185 (2013); translation from Teor. Mat. Fiz. 174, No. 2, 208-215 (2013).
Summary: We discuss mathematical aspects of the nonexistence of continuous (nontrivial) solutions of boundary value problems for equations of \(p\)-adic closed and open strings in the one-dimensional case. We find that the number of sign changes of the solution \(\psi(t)\) is not equal to the order of zeros of the function \(\psi^n(t)\) and that nonnegative (nonpositive) solutions do not exist. In the case of even \(n\), if a solution \(\psi\) exists, then the orders of zeros of the function \(\psi^n\) and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form \(2(2r+1)\), \(r\geq 0\).
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 11E95 | \(p\)-adic theory |
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
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