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16. Operadic interpretation of closed string field theory String theory deals with particles as maps of an interval into space (open strings) or of a circle into space (closed strings). e. a path space or a free loop space. The algebra of such fields is quite subtle since it is not given by pointwise multiplication of functions but rather is a convolution algebra derived from a (partially defined) product/composition of strings. Further, as strings evolve in space-time, they trace out world sheets, that is, maps of a Riemann surface with boundary into spacetime.
3. 7. 1). 16. Operadic interpretation of closed string field theory String theory deals with particles as maps of an interval into space (open strings) or of a circle into space (closed strings). e. a path space or a free loop space. The algebra of such fields is quite subtle since it is not given by pointwise multiplication of functions but rather is a convolution algebra derived from a (partially defined) product/composition of strings. Further, as strings evolve in space-time, they trace out world sheets, that is, maps of a Riemann surface with boundary into spacetime.
Ma-1(n)), (m 1,... ,mn) := Q(m1,... then Q,,,,, In is defined to be one-to-one monotonic from the ith subinterval {jl j of the partition (mi) onto the w(i)th subinterval {k( mi +... + m'Q(i)_1 < k < ml of the partition (m,D. -1(i), ,m+-1(n)Tmi,. ,m,,. 3. For the purposes of this example, we will represent an element aEEnbythe2xnmatrix 1 2 a(1) a(2) ... n U(n) If n = 3, m = 7, (ml, m2i m3) = (2, 2, 3) and a _ 1 2 3 3 2 1 then (mi, ms, ms) = (3, 2, 2). The subintervals determined by m and m' are respectively (12 134 1567) and (123 1 45 1 67).